Назад
ГДЗ Алгебра 7 клас Мерзляк (2024)
§ 1. Алгебраїчні вирази
Реклама:
Подайте у вигляді добутку вираз:
1) (5x – y2)(5x + y2) – 2(15x – 7y2) – 40 = 25x2 – y4 – 30x + 14y2 – 40 = (25x2 – 30x + 9) – (y4 – 14y2 + 49) = (5x – 3)2 – (y2 – 7)2 = (5x – 3 – y2 + 7)(5x – 3 + y2 – 7) = (5x – y2 + 4)(5x + y2 – 10);
2) (3m – 2n)(12m + 5n) + 3m(3n + 4) – 2(3n2 – 20n + 12) = 36m2 + 15mn – 24mn – 10n2 + 9mn + 12m – 6n2 + 40n – 24 = 36m2 – 16n2 + 12m + 40n – 24 = (36m2 + 12m + 1) – (16n2 – 40n + 25) = (6m + 1)2 – (4n – 5)2 = (6m + 1 – 4n + 5)(6m + 1 + 4n – 5) = (6m – 4n + 6)(6m + 4n – 4) = 4(3m – 2n + 3)(3m + 2n – 2).
1) (5x – y2)(5x + y2) – 2(15x – 7y2) – 40 = 25x2 – y4 – 30x + 14y2 – 40 = (25x2 – 30x + 9) – (y4 – 14y2 + 49) = (5x – 3)2 – (y2 – 7)2 = (5x – 3 – y2 + 7)(5x – 3 + y2 – 7) = (5x – y2 + 4)(5x + y2 – 10);
2) (3m – 2n)(12m + 5n) + 3m(3n + 4) – 2(3n2 – 20n + 12) = 36m2 + 15mn – 24mn – 10n2 + 9mn + 12m – 6n2 + 40n – 24 = 36m2 – 16n2 + 12m + 40n – 24 = (36m2 + 12m + 1) – (16n2 – 40n + 25) = (6m + 1)2 – (4n – 5)2 = (6m + 1 – 4n + 5)(6m + 1 + 4n – 5) = (6m – 4n + 6)(6m + 4n – 4) = 4(3m – 2n + 3)(3m + 2n – 2).