ГДЗ Алгебра 7 класс Мерзляк, Полонский, Якир. Номер 735

ОТВЕТЫ К ЗАДАНИЯМ

Разложите на множители многочлен:
1)

x^{2} - 4 x + 3

;

2)

a^{2} + 2 a - 24

;

3)

y^{2} + 12 y + 35

;

4)

x^{2} + x - 6

;

5)

c^{2} + 8 c d + 15 d^{2}

;

6)

9 x^{2} - 30 x y + 16 y^{2}

x^{2} - 4 x + 3 = x^{2} - 4 x + 4 - 1 = (x^{2} - 4 x + 4) - 1 = (x - 2)^{2} - 1 = (x - 2 - 1) (x - 2 + 1) = (x - 3) (x - 1)

a^{2} + 2 a - 24 = a^{2} + 2 a - 25 + 1 = (a^{2} + 2 a + 1) - 25 = (a + 1)^{2} - 5^{2} = (a + 1 - 5) (a + 1 + 5) = (a - 4) (a + 6)

y^{2} + 12 y + 35 = y^{2} + 12 y + 36 - 1 = (y^{2} + 12 y + 36) - 1 = (y + 6)^{2} - 1 = (y + 6 - 1) (y + 6 + 1) = (y + 5) (y + 7)

x^{2} + x - 6 = x^{2} + x - 6, 25 + 0, 25 = (x^{2} + x + 0, 25) - 6, 25 = (x + 0, 5)^{2} - 2, 5^{2} = (x + 0, 5 - 2, 5) (x + 0, 5 + 2, 5) = (x - 2) (x + 3)

c^{2} + 8 c d + 15 d^{2} = c^{2} + 8 c d + 16 d^{2} - d^{2} = (c^{2} + 8 c d + 16 d^{2}) - d^{2} = (c + 4 d)^{2} - d^{2} = (c + 4 d - d) (c + 4 d + d) = (c + 3 d) (c + 5 d)

9 x^{2} - 30 x y + 16 y^{2} = 9 x^{2} - 30 x y + 25 y^{2} - 9 y^{2} = (9 x^{2} - 30 x y + 25 y^{2}) - 9 y^{2} = (3 x - 5 y)^{2} - (3 y)^{2} = (3 x - 5 y - 3 y) (3 x - 5 y + 3 y) = (3 x - 8 y) (3 x - 2 y)