Разложите на множители:
а) $2x^3 - 2xy^2 - 6x^2 + 6y^2$;
б) $5a^2 - 5b^2 - 10a^3b + 10ab^3$;
в) $36x^3 - 144x - 36x^2 + 144$;
г) $y^3 + ay^2 - b^2y - b^2a$.
$2x^3 - 2xy^2 - 6x^2 + 6y^2 = (2x^3 - 2xy^2) - (6x^2 - 6y^2) = 2x(x^2 - y^2) - 6(x^2 - y^2) = (x^2 - y^2)(2x - 6) = 2(x - y)(x + y)(x - 3)$
$5a^2 - 5b^2 - 10a^3b + 10ab^3 = (5a^2 - 5b^2) - (10a^3b - 10ab^3) = 5(a^2 - b^2) - 10ab(a^2 - b^2) = (a^2 - b^2)(5 - 10ab) = 5(a - b)(a + b)(1 - 2ab)$
$36x^3 - 144x - 36x^2 + 144 = (36x^3 - 36x^2) - (144x - 144) = 36x^2(x - 1) - 144(x - 1) = (x - 1)(36x^2 - 144) = 36(x - 1)(x^2 - 4) = 36(x - 1)(x - 2)(x + 2)$
$y^3 + ay^2 - b^2y - b^2a = (y^3 + ay^2) - (b^2y + b^2a) = y^2(y + a) - b^2(y + a) = (y + a)(y^2 - b^2) = (y + a)(y - b)(y + b)$
Пожауйста, оцените решение
