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Номер 580, страница 105 - гдз по алгебре 7 класс учебник Мерзляк, Полонский
Авторы: Мерзляк А. Г., Полонский В. Б., Якир М. С.
Тип: Учебник
Издательство: Просвещение, Вентана-граф
Год издания: 2016 - 2022
ISBN: 978-5-360-07440-3
Рекомендовано Министерством образования и науки Российской Федерации
Популярные ГДЗ в 7 классе
Глава 2. Целые выражения. §16. Квадрат суммы и квадарт разности двух выражений - номер 580, страница 105.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1376130 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "105" "field_page_end" => null "field_url" => "/7-klass/algebra/merzlyak-uchebnik/580" "field_display_title" => "580" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1375417 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Целые выражения" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "30" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 864 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => "2022" "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для общеобразовательных организаций" "field_allowed" => "Рекомендовано Министерством образования и науки Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1407" "field_priority" => null "field_default_folder" => "/algebra_07/merzlyak/" "field_isbn" => "978-5-360-07440-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_url" => "/7-klass/algebra/merzlyak-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 864 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => "2022" "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для общеобразовательных организаций" "field_allowed" => "Рекомендовано Министерством образования и науки Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1407" "field_priority" => null "field_default_folder" => "/algebra_07/merzlyak/" "field_isbn" => "978-5-360-07440-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_url" => "/7-klass/algebra/merzlyak-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1375417 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Целые выражения" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "30" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:2 [ 0 => App\Models\Branch {#1118 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1375417 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Целые выражения" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1122 #items: array:1 [ 0 => App\Models\Term {#1119 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "30" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Book {#1121 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 864 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Term {#1120 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1124 #items: array:1 [ 0 => App\Models\Term {#1125 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:2 [ 0 => App\Models\Term {#1127 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1128 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1129 #items: array:3 [ 0 => App\Models\Term {#1130 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1131 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1132 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1133 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ 0 => App\Models\Term {#1135 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Term {#1137 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1140 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1143 #items: array:1 [ 0 => App\Models\Term {#1144 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => "2022" "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для общеобразовательных организаций" "field_allowed" => "Рекомендовано Министерством образования и науки Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1407" "field_priority" => null "field_default_folder" => "/algebra_07/merzlyak/" "field_isbn" => "978-5-360-07440-3" "field_cover" => array:1 [ 0 => "/media/algebra_07/merzlyak/covers/cover1.webp?ts=1757498550" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_07/merzlyak/covers/cover1.webp?ts=1757498550" "alt" => "" "width" => "600" "height" => "780" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1148 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1149 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/algebra/merzlyak-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 542 "class_subject" => 384 ] ] #original: array:50 [ "id" => 864 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1123} "field_class" => Illuminate\Database\Eloquent\Collection {#1124} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1126} "field_author" => Illuminate\Database\Eloquent\Collection {#1129} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1133} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1134} "field_country" => Illuminate\Database\Eloquent\Collection {#1136} "field_city" => Illuminate\Database\Eloquent\Collection {#1138} "field_series" => Illuminate\Database\Eloquent\Collection {#1140} "field_umk" => Illuminate\Database\Eloquent\Collection {#1141} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1142} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1143} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1145} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1146} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => "2022" "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для общеобразовательных организаций" "field_allowed" => "Рекомендовано Министерством образования и науки Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1407" "field_priority" => null "field_default_folder" => "/algebra_07/merzlyak/" "field_isbn" => "978-5-360-07440-3" "field_cover" => array:1 [ 0 => "/media/algebra_07/merzlyak/covers/cover1.webp?ts=1757498550" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_07/merzlyak/covers/cover1.webp?ts=1757498550" "alt" => "" "width" => "600" "height" => "780" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1147} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1148} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1149} "field_url" => "/7-klass/algebra/merzlyak-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1150} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 542 "class_subject" => 384 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1375417 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Целые выражения" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1122} "field_page_start" => "30" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1153} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1151} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1152 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1375443 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "§16. Квадрат суммы и квадарт разности двух выражений" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1154 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "102" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Book {#1121} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1156 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1375443 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "§16. Квадрат суммы и квадарт разности двух выражений" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1154} "field_page_start" => "102" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1155} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1156} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1107 #items: array:7 [ 0 => App\Models\Element {#1096 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1603982 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Edition {#1094 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5757 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5757 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "text" => "<p><strong>580.</strong> Выполните возведение в квадрат:</p><p><strong>1)</strong> $(10a^2 - 7ab^2)^2$;</p><p><strong>2)</strong> $(0,8b^3 + 0,2b^2c^4)^2$;</p><p><strong>3)</strong> $(30m^3n + 0,04n^2)^2$;</p><p><strong>4)</strong> $(0,5x^4y^5 - 20y^6)^2$;</p><p><strong>5)</strong> $(1\frac{1}{3}a^2b + 2\frac{1}{4}ab^2)^2$;</p><p><strong>6)</strong> $(2\frac{1}{3}x^3y^2 - \frac{9}{14}y^8x)^2$;</p><p><strong>7)</strong> $(15m^9 + \frac{5}{6}m^3)^2$;</p><p><strong>8)</strong> $(3\frac{1}{8}x^8y^{10} + \frac{16}{25}x^2y^6)^2$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "580-1.jpg" "alt" => null "width" => "513" "height" => 208 "path" => "/media/algebra_07/merzlyak/0-00/580-1.webp?ts=1757507083" ] ] ] #original: array:7 [ "id" => 1603982 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1088} "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "text" => "<p><strong>580.</strong> Выполните возведение в квадрат:</p><p><strong>1)</strong> $(10a^2 - 7ab^2)^2$;</p><p><strong>2)</strong> $(0,8b^3 + 0,2b^2c^4)^2$;</p><p><strong>3)</strong> $(30m^3n + 0,04n^2)^2$;</p><p><strong>4)</strong> $(0,5x^4y^5 - 20y^6)^2$;</p><p><strong>5)</strong> $(1\frac{1}{3}a^2b + 2\frac{1}{4}ab^2)^2$;</p><p><strong>6)</strong> $(2\frac{1}{3}x^3y^2 - \frac{9}{14}y^8x)^2$;</p><p><strong>7)</strong> $(15m^9 + \frac{5}{6}m^3)^2$;</p><p><strong>8)</strong> $(3\frac{1}{8}x^8y^{10} + \frac{16}{25}x^2y^6)^2$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "580-1.jpg" "alt" => null "width" => "513" "height" => 208 "path" => "/media/algebra_07/merzlyak/0-00/580-1.webp?ts=1757507083" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1168 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1608880 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1178 #items: array:1 [ 0 => App\Models\Edition {#1169 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5758 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5758 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "img" => array:8 [ 0 => array:5 [ "name" => "580-1.png" "alt" => null "width" => "720" "height" => 882 "path" => "/media/algebra_07/merzlyak/1-00/580-1.webp?ts=1757508240" ] 1 => array:5 [ "name" => "580-2.png" "alt" => null "width" => "720" "height" => 882 "path" => "/media/algebra_07/merzlyak/1-00/580-2.webp?ts=1757508240" ] 2 => array:5 [ "name" => "580-3.png" "alt" => null "width" => "720" "height" => 882 "path" => "/media/algebra_07/merzlyak/1-00/580-3.webp?ts=1757508240" ] 3 => array:5 [ "name" => "580-4.png" "alt" => null "width" => "720" "height" => 882 "path" => "/media/algebra_07/merzlyak/1-00/580-4.webp?ts=1757508240" ] 4 => array:5 [ "name" => "580-5.png" "alt" => null "width" => "720" "height" => 1244 "path" => "/media/algebra_07/merzlyak/1-00/580-5.webp?ts=1757508240" ] 5 => array:5 [ "name" => "580-6.png" "alt" => null "width" => "720" "height" => 1244 "path" => "/media/algebra_07/merzlyak/1-00/580-6.webp?ts=1757508240" ] 6 => array:5 [ "name" => "580-7.png" "alt" => null "width" => "720" "height" => 952 "path" => "/media/algebra_07/merzlyak/1-00/580-7.webp?ts=1757508240" ] 7 => array:5 [ "name" => "580-8.png" "alt" => null "width" => "720" "height" => 1257 "path" => "/media/algebra_07/merzlyak/1-00/580-8.webp?ts=1757508240" ] ] ] #original: array:6 [ "id" => 1608880 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1178} "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "img" => array:8 [ 0 => array:5 [ "name" => "580-1.png" "alt" => null "width" => "720" "height" => 882 "path" => "/media/algebra_07/merzlyak/1-00/580-1.webp?ts=1757508240" ] 1 => array:5 [ "name" => "580-2.png" "alt" => null "width" => "720" "height" => 882 "path" => "/media/algebra_07/merzlyak/1-00/580-2.webp?ts=1757508240" ] 2 => array:5 [ "name" => "580-3.png" "alt" => null "width" => "720" "height" => 882 "path" => "/media/algebra_07/merzlyak/1-00/580-3.webp?ts=1757508240" ] 3 => array:5 [ "name" => "580-4.png" "alt" => null "width" => "720" "height" => 882 "path" => "/media/algebra_07/merzlyak/1-00/580-4.webp?ts=1757508240" ] 4 => array:5 [ "name" => "580-5.png" "alt" => null "width" => "720" "height" => 1244 "path" => "/media/algebra_07/merzlyak/1-00/580-5.webp?ts=1757508240" ] 5 => array:5 [ "name" => "580-6.png" "alt" => null "width" => "720" "height" => 1244 "path" => "/media/algebra_07/merzlyak/1-00/580-6.webp?ts=1757508240" ] 6 => array:5 [ "name" => "580-7.png" "alt" => null "width" => "720" "height" => 952 "path" => "/media/algebra_07/merzlyak/1-00/580-7.webp?ts=1757508240" ] 7 => array:5 [ "name" => "580-8.png" "alt" => null "width" => "720" "height" => 1257 "path" => "/media/algebra_07/merzlyak/1-00/580-8.webp?ts=1757508240" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1089 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1604459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1078 #items: array:1 [ 0 => App\Models\Edition {#1085 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5759 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5759 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "580-1.jpg" "alt" => null "width" => "843" "height" => 758 "path" => "/media/algebra_07/merzlyak/2-00/580-1.webp?ts=1757507115" ] ] ] #original: array:6 [ "id" => 1604459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1078} "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "580-1.jpg" "alt" => null "width" => "843" "height" => 758 "path" => "/media/algebra_07/merzlyak/2-00/580-1.webp?ts=1757507115" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Element {#1080 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1604580 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:1 [ 0 => App\Models\Edition {#1081 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5760 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1075 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1073 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1109 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5760 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1075 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1073 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1109 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "580-1.png" "alt" => null "width" => "1400" "height" => 1311 "path" => "/media/algebra_07/merzlyak/3-00/580-1.webp?ts=1757507129" ] ] ] #original: array:6 [ "id" => 1604580 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1111} "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "580-1.png" "alt" => null "width" => "1400" "height" => 1311 "path" => "/media/algebra_07/merzlyak/3-00/580-1.webp?ts=1757507129" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Element {#1160 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1605434 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1170 #items: array:1 [ 0 => App\Models\Edition {#1161 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1166 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1166 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "580-1.jpg" "alt" => null "width" => "859" "height" => 862 "path" => "/media/algebra_07/merzlyak/4-00/580-1.webp?ts=1757507132" ] ] ] #original: array:6 [ "id" => 1605434 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1170} "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "580-1.jpg" "alt" => null "width" => "859" "height" => 862 "path" => "/media/algebra_07/merzlyak/4-00/580-1.webp?ts=1757507132" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Element {#1117 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1604816 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1162 #items: array:1 [ 0 => App\Models\Edition {#1113 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5762 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 5" "field_order" => "6" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" …7 ] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "580-1.jpg" "alt" => null "width" => "594" "height" => 1609 "path" => "/media/algebra_07/merzlyak/5-00/580-1.webp?ts=1757507082" ] ] ] #original: array:6 [ "id" => 1604816 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1162} "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "580-1.jpg" "alt" => null "width" => "594" "height" => 1609 "path" => "/media/algebra_07/merzlyak/5-00/580-1.webp?ts=1757507082" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Element {#1176 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1793653 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1186 #items: array:1 [ 0 => App\Models\Edition {#1177 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "text" => "<p><strong>1)</strong> Для возведения в квадрат выражения $(10a^2 - 7ab^2)^2$ используем формулу квадрата разности: $(x-y)^2 = x^2 - 2xy + y^2$.<br>В нашем случае $x = 10a^2$ и $y = 7ab^2$.<br>Квадрат первого члена: $(10a^2)^2 = 100a^4$.<br>Удвоенное произведение первого и второго членов: $2 \cdot 10a^2 \cdot 7ab^2 = 140a^3b^2$.<br>Квадрат второго члена: $(7ab^2)^2 = 49a^2b^4$.<br>Следовательно, $(10a^2 - 7ab^2)^2 = 100a^4 - 140a^3b^2 + 49a^2b^4$.<br>Ответ: $100a^4 - 140a^3b^2 + 49a^2b^4$.</p><p><strong>2)</strong> Для возведения в квадрат выражения $(0,8b^3 + 0,2b^2c^4)^2$ используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.<br>Здесь $x = 0,8b^3$ и $y = 0,2b^2c^4$.<br>Квадрат первого члена: $(0,8b^3)^2 = 0,64b^6$.<br>Удвоенное произведение первого и второго членов: $2 \cdot 0,8b^3 \cdot 0,2b^2c^4 = 0,32b^5c^4$.<br>Квадрат второго члена: $(0,2b^2c^4)^2 = 0,04b^4c^8$.<br>Следовательно, $(0,8b^3 + 0,2b^2c^4)^2 = 0,64b^6 + 0,32b^5c^4 + 0,04b^4c^8$.<br>Ответ: $0,64b^6 + 0,32b^5c^4 + 0,04b^4c^8$.</p><p><strong>3)</strong> Для возведения в квадрат выражения $(30m^3n + 0,04n^2)^2$ используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.<br>Здесь $x = 30m^3n$ и $y = 0,04n^2$.<br>Квадрат первого члена: $(30m^3n)^2 = 900m^6n^2$.<br>Удвоенное произведение первого и второго членов: $2 \cdot 30m^3n \cdot 0,04n^2 = 2,4m^3n^3$.<br>Квадрат второго члена: $(0,04n^2)^2 = 0,0016n^4$.<br>Следовательно, $(30m^3n + 0,04n^2)^2 = 900m^6n^2 + 2,4m^3n^3 + 0,0016n^4$.<br>Ответ: $900m^6n^2 + 2,4m^3n^3 + 0,0016n^4$.</p><p><strong>4)</strong> Для возведения в квадрат выражения $(0,5x^4y^5 - 20y^6)^2$ используем формулу квадрата разности: $(x-y)^2 = x^2 - 2xy + y^2$.<br>Здесь $x = 0,5x^4y^5$ и $y = 20y^6$.<br>Квадрат первого члена: $(0,5x^4y^5)^2 = 0,25x^8y^{10}$.<br>Удвоенное произведение первого и второго членов: $2 \cdot 0,5x^4y^5 \cdot 20y^6 = 20x^4y^{11}$.<br>Квадрат второго члена: $(20y^6)^2 = 400y^{12}$.<br>Следовательно, $(0,5x^4y^5 - 20y^6)^2 = 0,25x^8y^{10} - 20x^4y^{11} + 400y^{12}$.<br>Ответ: $0,25x^8y^{10} - 20x^4y^{11} + 400y^{12}$.</p><p><strong>5)</strong> Сначала преобразуем смешанные числа в неправильные дроби: $1\frac{1}{3} = \frac{4}{3}$ и $2\frac{1}{4} = \frac{9}{4}$.<br>Выражение принимает вид: $(\frac{4}{3}a^2b + \frac{9}{4}ab^2)^2$.<br>Используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.<br>Здесь $x = \frac{4}{3}a^2b$ и $y = \frac{9}{4}ab^2$.<br>Квадрат первого члена: $(\frac{4}{3}a^2b)^2 = \frac{16}{9}a^4b^2$.<br>Удвоенное произведение: $2 \cdot \frac{4}{3}a^2b \cdot \frac{9}{4}ab^2 = 2 \cdot \frac{36}{12}a^3b^3 = 6a^3b^3$.<br>Квадрат второго члена: $(\frac{9}{4}ab^2)^2 = \frac{81}{16}a^2b^4$.<br>Следовательно, $(1\frac{1}{3}a^2b + 2\frac{1}{4}ab^2)^2 = \frac{16}{9}a^4b^2 + 6a^3b^3 + \frac{81}{16}a^2b^4$.<br>Ответ: $\frac{16}{9}a^4b^2 + 6a^3b^3 + \frac{81}{16}a^2b^4$.</p><p><strong>6)</strong> Сначала преобразуем смешанное число в неправильную дробь: $2\frac{1}{3} = \frac{7}{3}$.<br>Выражение принимает вид: $(\frac{7}{3}x^3y^2 - \frac{9}{14}y^8x)^2$.<br>Используем формулу квадрата разности: $(x-y)^2 = x^2 - 2xy + y^2$.<br>Здесь $x = \frac{7}{3}x^3y^2$ и $y = \frac{9}{14}xy^8$.<br>Квадрат первого члена: $(\frac{7}{3}x^3y^2)^2 = \frac{49}{9}x^6y^4$.<br>Удвоенное произведение: $2 \cdot \frac{7}{3}x^3y^2 \cdot \frac{9}{14}xy^8 = 2 \cdot \frac{63}{42}x^4y^{10} = 2 \cdot \frac{3}{2}x^4y^{10} = 3x^4y^{10}$.<br>Квадрат второго члена: $(\frac{9}{14}xy^8)^2 = \frac{81}{196}x^2y^{16}$.<br>Следовательно, $(2\frac{1}{3}x^3y^2 - \frac{9}{14}y^8x)^2 = \frac{49}{9}x^6y^4 - 3x^4y^{10} + \frac{81}{196}x^2y^{16}$.<br>Ответ: $\frac{49}{9}x^6y^4 - 3x^4y^{10} + \frac{81}{196}x^2y^{16}$.</p><p><strong>7)</strong> Для возведения в квадрат выражения $(15m^9 + \frac{5}{6}m^3)^2$ используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.<br>Здесь $x = 15m^9$ и $y = \frac{5}{6}m^3$.<br>Квадрат первого члена: $(15m^9)^2 = 225m^{18}$.<br>Удвоенное произведение первого и второго членов: $2 \cdot 15m^9 \cdot \frac{5}{6}m^3 = \frac{150}{6}m^{12} = 25m^{12}$.<br>Квадрат второго члена: $(\frac{5}{6}m^3)^2 = \frac{25}{36}m^6$.<br>Следовательно, $(15m^9 + \frac{5}{6}m^3)^2 = 225m^{18} + 25m^{12} + \frac{25}{36}m^6$.<br>Ответ: $225m^{18} + 25m^{12} + \frac{25}{36}m^6$.</p><p><strong>8)</strong> Сначала преобразуем смешанное число в неправильную дробь: $3\frac{1}{8} = \frac{25}{8}$.<br>Выражение принимает вид: $(\frac{25}{8}x^8y^{10} + \frac{16}{25}x^2y^6)^2$.<br>Используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.<br>Здесь $x = \frac{25}{8}x^8y^{10}$ и $y = \frac{16}{25}x^2y^6$.<br>Квадрат первого члена: $(\frac{25}{8}x^8y^{10})^2 = \frac{625}{64}x^{16}y^{20}$.<br>Удвоенное произведение: $2 \cdot \frac{25}{8}x^8y^{10} \cdot \frac{16}{25}x^2y^6 = 2 \cdot \frac{16}{8}x^{10}y^{16} = 4x^{10}y^{16}$.<br>Квадрат второго члена: $(\frac{16}{25}x^2y^6)^2 = \frac{256}{625}x^4y^{12}$.<br>Следовательно, $(3\frac{1}{8}x^8y^{10} + \frac{16}{25}x^2y^6)^2 = \frac{625}{64}x^{16}y^{20} + 4x^{10}y^{16} + \frac{256}{625}x^4y^{12}$.<br>Ответ: $\frac{625}{64}x^{16}y^{20} + 4x^{10}y^{16} + \frac{256}{625}x^4y^{12}$.</p>" ] #original: array:6 [ "id" => 1793653 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1186} "task" => array:2 [ "refs" => "1376130" "type" => "task" ] "text" => "<p><strong>1)</strong> Для возведения в квадрат выражения $(10a^2 - 7ab^2)^2$ используем формулу квадрата разности: $(x-y)^2 = x^2 - 2xy + y^2$.<br>В нашем случае $x = 10a^2$ и $y = 7ab^2$.<br>Квадрат первого члена: $(10a^2)^2 = 100a^4$.<br>Удвоенное произведение первого и второго членов: $2 \cdot 10a^2 \cdot 7ab^2 = 140a^3b^2$.<br>Квадрат второго члена: $(7ab^2)^2 = 49a^2b^4$.<br>Следовательно, $(10a^2 - 7ab^2)^2 = 100a^4 - 140a^3b^2 + 49a^2b^4$.<br>Ответ: $100a^4 - 140a^3b^2 + 49a^2b^4$.</p><p><strong>2)</strong> Для возведения в квадрат выражения $(0,8b^3 + 0,2b^2c^4)^2$ используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.<br>Здесь $x = 0,8b^3$ и $y = 0,2b^2c^4$.<br>Квадрат первого члена: $(0,8b^3)^2 = 0,64b^6$.<br>Удвоенное произведение первого и второго членов: $2 \cdot 0,8b^3 \cdot 0,2b^2c^4 = 0,32b^5c^4$.<br>Квадрат второго члена: $(0,2b^2c^4)^2 = 0,04b^4c^8$.<br>Следовательно, $(0,8b^3 + 0,2b^2c^4)^2 = 0,64b^6 + 0,32b^5c^4 + 0,04b^4c^8$.<br>Ответ: $0,64b^6 + 0,32b^5c^4 + 0,04b^4c^8$.</p><p><strong>3)</strong> Для возведения в квадрат выражения $(30m^3n + 0,04n^2)^2$ используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.<br>Здесь $x = 30m^3n$ и $y = 0,04n^2$.<br>Квадрат первого члена: $(30m^3n)^2 = 900m^6n^2$.<br>Удвоенное произведение первого и второго членов: $2 \cdot 30m^3n \cdot 0,04n^2 = 2,4m^3n^3$.<br>Квадрат второго члена: $(0,04n^2)^2 = 0,0016n^4$.<br>Следовательно, $(30m^3n + 0,04n^2)^2 = 900m^6n^2 + 2,4m^3n^3 + 0,0016n^4$.<br>Ответ: $900m^6n^2 + 2,4m^3n^3 + 0,0016n^4$.</p><p><strong>4)</strong> Для возведения в квадрат выражения $(0,5x^4y^5 - 20y^6)^2$ используем формулу квадрата разности: $(x-y)^2 = x^2 - 2xy + y^2$.<br>Здесь $x = 0,5x^4y^5$ и $y = 20y^6$.<br>Квадрат первого члена: $(0,5x^4y^5)^2 = 0,25x^8y^{10}$.<br>Удвоенное произведение первого и второго членов: $2 \cdot 0,5x^4y^5 \cdot 20y^6 = 20x^4y^{11}$.<br>Квадрат второго члена: $(20y^6)^2 = 400y^{12}$.<br>Следовательно, $(0,5x^4y^5 - 20y^6)^2 = 0,25x^8y^{10} - 20x^4y^{11} + 400y^{12}$.<br>Ответ: $0,25x^8y^{10} - 20x^4y^{11} + 400y^{12}$.</p><p><strong>5)</strong> Сначала преобразуем смешанные числа в неправильные дроби: $1\frac{1}{3} = \frac{4}{3}$ и $2\frac{1}{4} = \frac{9}{4}$.<br>Выражение принимает вид: $(\frac{4}{3}a^2b + \frac{9}{4}ab^2)^2$.<br>Используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.<br>Здесь $x = \frac{4}{3}a^2b$ и $y = \frac{9}{4}ab^2$.<br>Квадрат первого члена: $(\frac{4}{3}a^2b)^2 = \frac{16}{9}a^4b^2$.<br>Удвоенное произведение: $2 \cdot \frac{4}{3}a^2b \cdot \frac{9}{4}ab^2 = 2 \cdot \frac{36}{12}a^3b^3 = 6a^3b^3$.<br>Квадрат второго члена: $(\frac{9}{4}ab^2)^2 = \frac{81}{16}a^2b^4$.<br>Следовательно, $(1\frac{1}{3}a^2b + 2\frac{1}{4}ab^2)^2 = \frac{16}{9}a^4b^2 + 6a^3b^3 + \frac{81}{16}a^2b^4$.<br>Ответ: $\frac{16}{9}a^4b^2 + 6a^3b^3 + \frac{81}{16}a^2b^4$.</p><p><strong>6)</strong> Сначала преобразуем смешанное число в неправильную дробь: $2\frac{1}{3} = \frac{7}{3}$.<br>Выражение принимает вид: $(\frac{7}{3}x^3y^2 - \frac{9}{14}y^8x)^2$.<br>Используем формулу квадрата разности: $(x-y)^2 = x^2 - 2xy + y^2$.<br>Здесь $x = \frac{7}{3}x^3y^2$ и $y = \frac{9}{14}xy^8$.<br>Квадрат первого члена: $(\frac{7}{3}x^3y^2)^2 = \frac{49}{9}x^6y^4$.<br>Удвоенное произведение: $2 \cdot \frac{7}{3}x^3y^2 \cdot \frac{9}{14}xy^8 = 2 \cdot \frac{63}{42}x^4y^{10} = 2 \cdot \frac{3}{2}x^4y^{10} = 3x^4y^{10}$.<br>Квадрат второго члена: $(\frac{9}{14}xy^8)^2 = \frac{81}{196}x^2y^{16}$.<br>Следовательно, $(2\frac{1}{3}x^3y^2 - \frac{9}{14}y^8x)^2 = \frac{49}{9}x^6y^4 - 3x^4y^{10} + \frac{81}{196}x^2y^{16}$.<br>Ответ: $\frac{49}{9}x^6y^4 - 3x^4y^{10} + \frac{81}{196}x^2y^{16}$.</p><p><strong>7)</strong> Для возведения в квадрат выражения $(15m^9 + \frac{5}{6}m^3)^2$ используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.<br>Здесь $x = 15m^9$ и $y = \frac{5}{6}m^3$.<br>Квадрат первого члена: $(15m^9)^2 = 225m^{18}$.<br>Удвоенное произведение первого и второго членов: $2 \cdot 15m^9 \cdot \frac{5}{6}m^3 = \frac{150}{6}m^{12} = 25m^{12}$.<br>Квадрат второго члена: $(\frac{5}{6}m^3)^2 = \frac{25}{36}m^6$.<br>Следовательно, $(15m^9 + \frac{5}{6}m^3)^2 = 225m^{18} + 25m^{12} + \frac{25}{36}m^6$.<br>Ответ: $225m^{18} + 25m^{12} + \frac{25}{36}m^6$.</p><p><strong>8)</strong> Сначала преобразуем смешанное число в неправильную дробь: $3\frac{1}{8} = \frac{25}{8}$.<br>Выражение принимает вид: $(\frac{25}{8}x^8y^{10} + \frac{16}{25}x^2y^6)^2$.<br>Используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.<br>Здесь $x = \frac{25}{8}x^8y^{10}$ и $y = \frac{16}{25}x^2y^6$.<br>Квадрат первого члена: $(\frac{25}{8}x^8y^{10})^2 = \frac{625}{64}x^{16}y^{20}$.<br>Удвоенное произведение: $2 \cdot \frac{25}{8}x^8y^{10} \cdot \frac{16}{25}x^2y^6 = 2 \cdot \frac{16}{8}x^{10}y^{16} = 4x^{10}y^{16}$.<br>Квадрат второго члена: $(\frac{16}{25}x^2y^6)^2 = \frac{256}{625}x^4y^{12}$.<br>Следовательно, $(3\frac{1}{8}x^8y^{10} + \frac{16}{25}x^2y^6)^2 = \frac{625}{64}x^{16}y^{20} + 4x^{10}y^{16} + \frac{256}{625}x^4y^{12}$.<br>Ответ: $\frac{625}{64}x^{16}y^{20} + 4x^{10}y^{16} + \frac{256}{625}x^4y^{12}$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: 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[] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1377286" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1377283" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1326 #items: array:9 [ 0 => App\Models\Task {#1342 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Task {#1348 #connection: 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+incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 7 => App\Models\Task {#1465 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true 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№580 (с. 105)
Условие. №580 (с. 105)
скриншот условия
580. Выполните возведение в квадрат:
1) $(10a^2 - 7ab^2)^2$;
2) $(0,8b^3 + 0,2b^2c^4)^2$;
3) $(30m^3n + 0,04n^2)^2$;
4) $(0,5x^4y^5 - 20y^6)^2$;
5) $(1\frac{1}{3}a^2b + 2\frac{1}{4}ab^2)^2$;
6) $(2\frac{1}{3}x^3y^2 - \frac{9}{14}y^8x)^2$;
7) $(15m^9 + \frac{5}{6}m^3)^2$;
8) $(3\frac{1}{8}x^8y^{10} + \frac{16}{25}x^2y^6)^2$.
Решение 1. №580 (с. 105)
Решение 2. №580 (с. 105)
Решение 3. №580 (с. 105)
Решение 4. №580 (с. 105)
Решение 5. №580 (с. 105)
Решение 6. №580 (с. 105)
1) Для возведения в квадрат выражения $(10a^2 - 7ab^2)^2$ используем формулу квадрата разности: $(x-y)^2 = x^2 - 2xy + y^2$.
В нашем случае $x = 10a^2$ и $y = 7ab^2$.
Квадрат первого члена: $(10a^2)^2 = 100a^4$.
Удвоенное произведение первого и второго членов: $2 \cdot 10a^2 \cdot 7ab^2 = 140a^3b^2$.
Квадрат второго члена: $(7ab^2)^2 = 49a^2b^4$.
Следовательно, $(10a^2 - 7ab^2)^2 = 100a^4 - 140a^3b^2 + 49a^2b^4$.
Ответ: $100a^4 - 140a^3b^2 + 49a^2b^4$.
2) Для возведения в квадрат выражения $(0,8b^3 + 0,2b^2c^4)^2$ используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.
Здесь $x = 0,8b^3$ и $y = 0,2b^2c^4$.
Квадрат первого члена: $(0,8b^3)^2 = 0,64b^6$.
Удвоенное произведение первого и второго членов: $2 \cdot 0,8b^3 \cdot 0,2b^2c^4 = 0,32b^5c^4$.
Квадрат второго члена: $(0,2b^2c^4)^2 = 0,04b^4c^8$.
Следовательно, $(0,8b^3 + 0,2b^2c^4)^2 = 0,64b^6 + 0,32b^5c^4 + 0,04b^4c^8$.
Ответ: $0,64b^6 + 0,32b^5c^4 + 0,04b^4c^8$.
3) Для возведения в квадрат выражения $(30m^3n + 0,04n^2)^2$ используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.
Здесь $x = 30m^3n$ и $y = 0,04n^2$.
Квадрат первого члена: $(30m^3n)^2 = 900m^6n^2$.
Удвоенное произведение первого и второго членов: $2 \cdot 30m^3n \cdot 0,04n^2 = 2,4m^3n^3$.
Квадрат второго члена: $(0,04n^2)^2 = 0,0016n^4$.
Следовательно, $(30m^3n + 0,04n^2)^2 = 900m^6n^2 + 2,4m^3n^3 + 0,0016n^4$.
Ответ: $900m^6n^2 + 2,4m^3n^3 + 0,0016n^4$.
4) Для возведения в квадрат выражения $(0,5x^4y^5 - 20y^6)^2$ используем формулу квадрата разности: $(x-y)^2 = x^2 - 2xy + y^2$.
Здесь $x = 0,5x^4y^5$ и $y = 20y^6$.
Квадрат первого члена: $(0,5x^4y^5)^2 = 0,25x^8y^{10}$.
Удвоенное произведение первого и второго членов: $2 \cdot 0,5x^4y^5 \cdot 20y^6 = 20x^4y^{11}$.
Квадрат второго члена: $(20y^6)^2 = 400y^{12}$.
Следовательно, $(0,5x^4y^5 - 20y^6)^2 = 0,25x^8y^{10} - 20x^4y^{11} + 400y^{12}$.
Ответ: $0,25x^8y^{10} - 20x^4y^{11} + 400y^{12}$.
5) Сначала преобразуем смешанные числа в неправильные дроби: $1\frac{1}{3} = \frac{4}{3}$ и $2\frac{1}{4} = \frac{9}{4}$.
Выражение принимает вид: $(\frac{4}{3}a^2b + \frac{9}{4}ab^2)^2$.
Используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.
Здесь $x = \frac{4}{3}a^2b$ и $y = \frac{9}{4}ab^2$.
Квадрат первого члена: $(\frac{4}{3}a^2b)^2 = \frac{16}{9}a^4b^2$.
Удвоенное произведение: $2 \cdot \frac{4}{3}a^2b \cdot \frac{9}{4}ab^2 = 2 \cdot \frac{36}{12}a^3b^3 = 6a^3b^3$.
Квадрат второго члена: $(\frac{9}{4}ab^2)^2 = \frac{81}{16}a^2b^4$.
Следовательно, $(1\frac{1}{3}a^2b + 2\frac{1}{4}ab^2)^2 = \frac{16}{9}a^4b^2 + 6a^3b^3 + \frac{81}{16}a^2b^4$.
Ответ: $\frac{16}{9}a^4b^2 + 6a^3b^3 + \frac{81}{16}a^2b^4$.
6) Сначала преобразуем смешанное число в неправильную дробь: $2\frac{1}{3} = \frac{7}{3}$.
Выражение принимает вид: $(\frac{7}{3}x^3y^2 - \frac{9}{14}y^8x)^2$.
Используем формулу квадрата разности: $(x-y)^2 = x^2 - 2xy + y^2$.
Здесь $x = \frac{7}{3}x^3y^2$ и $y = \frac{9}{14}xy^8$.
Квадрат первого члена: $(\frac{7}{3}x^3y^2)^2 = \frac{49}{9}x^6y^4$.
Удвоенное произведение: $2 \cdot \frac{7}{3}x^3y^2 \cdot \frac{9}{14}xy^8 = 2 \cdot \frac{63}{42}x^4y^{10} = 2 \cdot \frac{3}{2}x^4y^{10} = 3x^4y^{10}$.
Квадрат второго члена: $(\frac{9}{14}xy^8)^2 = \frac{81}{196}x^2y^{16}$.
Следовательно, $(2\frac{1}{3}x^3y^2 - \frac{9}{14}y^8x)^2 = \frac{49}{9}x^6y^4 - 3x^4y^{10} + \frac{81}{196}x^2y^{16}$.
Ответ: $\frac{49}{9}x^6y^4 - 3x^4y^{10} + \frac{81}{196}x^2y^{16}$.
7) Для возведения в квадрат выражения $(15m^9 + \frac{5}{6}m^3)^2$ используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.
Здесь $x = 15m^9$ и $y = \frac{5}{6}m^3$.
Квадрат первого члена: $(15m^9)^2 = 225m^{18}$.
Удвоенное произведение первого и второго членов: $2 \cdot 15m^9 \cdot \frac{5}{6}m^3 = \frac{150}{6}m^{12} = 25m^{12}$.
Квадрат второго члена: $(\frac{5}{6}m^3)^2 = \frac{25}{36}m^6$.
Следовательно, $(15m^9 + \frac{5}{6}m^3)^2 = 225m^{18} + 25m^{12} + \frac{25}{36}m^6$.
Ответ: $225m^{18} + 25m^{12} + \frac{25}{36}m^6$.
8) Сначала преобразуем смешанное число в неправильную дробь: $3\frac{1}{8} = \frac{25}{8}$.
Выражение принимает вид: $(\frac{25}{8}x^8y^{10} + \frac{16}{25}x^2y^6)^2$.
Используем формулу квадрата суммы: $(x+y)^2 = x^2 + 2xy + y^2$.
Здесь $x = \frac{25}{8}x^8y^{10}$ и $y = \frac{16}{25}x^2y^6$.
Квадрат первого члена: $(\frac{25}{8}x^8y^{10})^2 = \frac{625}{64}x^{16}y^{20}$.
Удвоенное произведение: $2 \cdot \frac{25}{8}x^8y^{10} \cdot \frac{16}{25}x^2y^6 = 2 \cdot \frac{16}{8}x^{10}y^{16} = 4x^{10}y^{16}$.
Квадрат второго члена: $(\frac{16}{25}x^2y^6)^2 = \frac{256}{625}x^4y^{12}$.
Следовательно, $(3\frac{1}{8}x^8y^{10} + \frac{16}{25}x^2y^6)^2 = \frac{625}{64}x^{16}y^{20} + 4x^{10}y^{16} + \frac{256}{625}x^4y^{12}$.
Ответ: $\frac{625}{64}x^{16}y^{20} + 4x^{10}y^{16} + \frac{256}{625}x^4y^{12}$.
Другие задания:
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