вправа 719 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) (a² + b²)² - 4a²b² =
= (a² + b² - 2ab)(a² + b² + 2ab) =
= (a - b)²(a + b)²;
2) 81 - (x² + 6x)² =
= (9 - (x² + 6x))(9 + (x² + 6x)) =
= (9 - x² - 6x)(3 + x)²;
3) a² + 2ab + b² - c² =
= (a + b)² - c² =
= (a + b - c)(a + b + c);
4) c² + 4c + 4 - k² =
= (c + 2)² - k² =
= (c + 2 - k)(c + 2 + k);
5) 9a² + c² + 6ac - 9 =
= (3a + c)² - 9 =
= (3a + c - 3)(3a + c + 3);
6) a² - b² - 10b - 25 =
= a² - (b - 5)² =
= (a - (b - 5))(a + (b - 5)) =
= (a - b + 5)(a + b - 5);
7) 49 - y² + x² - 14x =
= (x - 7)² - y² =
= (x - 7 - y)(x - 7 + y);
8) mn² - m³ - 12m² - 36m =
= m(n² - (m² + 12m + 36)) =
= m(n² - (m + 6)²) =
= m(n - (m + 6))(n + (m + 6)) =
= m(n - m - 6)(n + m + 6).