Question

8. Разложите на множители.
1) a² b + ab² + 8a + 8b
4) x² + 3x - 4x-12
7) 35x² + 21x - 10x - 6
10) a³ + ab + a b² + b3​

Answer 1

Ответ:

a^2b + ab^2 + 8a + 8ba

2

b+ab

2

+8a+8b = a(a + 8) + b(a + 8)a(a+8)+b(a+8) = (a + b)(a + 8)(a+b)(a+8)

x^2 + 3x - 4x - 12x

2

+3x−4x−12 = x(x + 3) - 4(x + 3)x(x+3)−4(x+3) = (x - 4)(x + 3)(x−4)(x+3)

35x^2 + 21x - 10x - 635x

2

+21x−10x−6 = 7x(5x + 3) - 2(5x + 3)7x(5x+3)−2(5x+3) = (7x - 2)(5x + 3)(7x−2)(5x+3)

a^3 + ab + ab^2 + b^3a

3

+ab+ab

2

+b

3

= a(a^2 + b) + b(a^2 + b)a(a

2

+b)+b(a

2

+b) = (a + b)(a^2 + b)(a+b)(a

2

+b)