вправа 717 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) 3ab + 15b - 3a - 15 =
= 3b(a + 5) - 3(a + 5) =
= (3b - 3)(a + 5) =
= 3(b - 1)(a + 5);
2) 84 - 42y - 7xy + 14x =
= 42(2 - y) + 7x(2 - y) =
= (42 + 7x)(2 - y) =
= 7(6 + x)(2 - y);
3) abc + 6ac + 8ab + 48a =
= ac(b + 6) + 8a(b + 6) =
= (ac + 8a)(b + 6) =
= a(c + 8)(b + 6);
4) m³ - m²n + m² - mn =
= m(m² - mn + m - n) =
= m(m(m - n) + (m - n)) =
= m(m + 1)(m - n);
5) a³ + a² - a - 1 =
= a²(a + 1) - (a + 1) =
= (a² - 1)(a + 1) =
= (a - 1)(a + 1)(a + 1) =
= (a - 1)(a + 1)²;
6) 2x³ - 2xy² - 8x² + 8y² =
= 2x²(x - 4) - 2y²(x - 4) =
= (2x² - 2y²)(x - 4) =
= 2(x² - y²)(x - 4) =
= 2(x - y)(x + y)(x - 4);
7) 5a² - 5b² - 15a³b + 15ab³ =
= 5a²(1 - 3ab) - 5b²(1 - 3ab) =
= (5a² - 5b²)(1 - 3ab) =
= 5(a² - b²)(1 - 3ab) =
= 5(a - b)(a + b)(1 - 3ab);
8) a²b² - 1 - b² + a² =
= b²(a² - 1) + (a² - 1) =
= (b² + 1)(a² - 1) =
= (b² + 1)(a - 1)(a + 1).