Разложите на множетели: 1) 12a^4+18a^2; 2) 2x^3-5x^2-6x+15; 3) 9a^2-4b^2 4) 36x^2-12xy+y^2

1) 12a^4 + 18a^2 = 6a^2 * (2a^2 + 3).

2) 2x^3 - 5x^2 - 6x + 15 = (2x^3 - 5x^2 - 6x) + 15 = x(2x^2 - 5x - 6x) + 15;

Пусть 2x^2 - 5x - 6x = 0;

D = 25 + 24 = 49;

x1 = 5 + 7/ 4 = 3;

x2 = 5 - 7/4 = -0,5;

x(x - 3)(x + 0,5) + 15.

3) 9a^2 - 4b^2 = (3a - 2b)(3a + 2b).

4) 36x^2 - 12xy + y^2 = (6x + y)^2.

5) 3a^3-48ac^2 = 3a(a^2 - 16c^2) = 3a(a - 4c)(a + 4c).

6) 81c^4 + 3b^3c = 3(27c^3 + b^3) = 3(3с + b)(9c^2 - 3cb + b^2).

7) a^2 - 9b^2 - a - 3b = a^2 - a - 9b^2 - 3b = a(a - 1) - 3b(b - 1).

8) 25c^2 - 4x^2 - 4x - 1 = (5c - 2x)(5c + 2x) - 4x - 1.

9) 27a^3 - 8 = (3a - 2)(9a^2 + 6a + 4).