вправа 734 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) x² - 10x + 24 =
= x² - 10x + 25 - 1 =
= (x - 5)² - 1² =
= (x - 5 - 1)(x - 5 + 1) =
= (x - 6)(x - 4);
2) a² + 4a - 32 =
= a² + 4a + 4 - 4 - 32 =
= (a + 2)² - 6² =
= (a + 2 - 6)(a + 2 + 6) =
= (a - 4)(a + 8);
3) b² - 3b - 4 =
= b² - 3b + 2,25 - 6,25 =
= (b - 1,5)² - 2,5² =
= (b - 1,5 - 2,5)(b - 1,5 + 2,5) =
= (b - 4)(b + 1);
4) 4a² - 12a + 5 =
= 4a² - 12a + 9 - 4 =
= (2a - 3)² - 2² =
= (2a - 3 - 2)(2a - 3 + 2) =
= (2a - 5)(2a - 1);
5) 9x² - 24xy + 7y² =
= 9x² - 24xy + 16y² - 9y² =
= (3x - 4y)² - (3y)² =
= (3x - 4y - 3y)(3x - 4y + 3y) =
= (3x - 7y)(3x - y);
6) 36m² - 60mn + 21n² =
= 36m² - 60mn + 25n² - 4n² =
= (6m - 5n)² - (2n)² =
= (6m - 5n - 2n)(6m - 5n + 2n) =
= (6m - 7n)(6m - 3n) =
= 3(2m - n)(6m - 7n).