вправа 735 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) x² - 4x + 3 =
= x² - 4x + 4 - 1 =
= (x - 2)² - 1² =
= (x - 2 - 1)(x - 2 + 1) =
= (x - 3)(x - 1);
2) a² + 2a - 24 =
= a² + 2a + 1 - 25 =
= (a + 1)² - 5² =
= (a + 1 - 5)(a + 1 + 5) =
= (a - 4)(a + 6);
3) y² + 12y + 35 =
= y² + 12y + 36 - 1 =
= (y + 6)² - 1² =
= (y + 6 - 1)(y + 6 + 1) =
= (y + 5)(y + 7);
4) x² + x - 6 =
= x² + x + 0,25 - 6,25 =
= (x + 0,5)² - 2,5² =
= (x + 0,5 - 2,5)(x + 0,5 + 2,5) =
= (x - 2)(x + 3);
5) c² + 8cd + 15d² =
= c² + 8cd + 16d² - d² =
= (c + 4d)² - d² =
= (c + 4d - d)(c + 4d + d) =
= (c + 3d)(c + 5d);
6) 9x² - 30xy + 16y² =
= 9x² - 30xy + 25y² - 9y² =
= (3x - 5y)² - (3y)² =
= (3x - 5y - 3y)(3x - 5y + 3y) =
= (3x - 8y)(3x - 2y).