因数 (2a-b)(2x-2y)^2-(6a-3b)^3(x-y)

解

因数

(2 a - b) (2 x - 2 y)^{2} - (6 a - 3 b)^{3} (x - y)

(- b + 2 a) (x - y) (4 (x - y) - 27 (- b + 2 a)^{2})

解答ステップ

(2 a - b) (2 x - 2 y)^{2} - (6 a - 3 b)^{3} (x - y)

(2 a - b) (2 x - 2 y)^{2} = 4 (2 a - b) (x - y)^{2}

(6 a - 3 b)^{3} (x - y) = 3^{3} (2 a - b)^{3} (x - y)

= 4 (2 a - b) (x - y)^{2} - 3^{3} (2 a - b)^{3} (x - y)

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

(x - y)^{2} = (x - y) (x - y), (- b + 2 a)^{3} = (- b + 2 a) (- b + 2 a)^{2}

= 4 (- b + 2 a) (x - y) (x - y) - 27 (- b + 2 a) (- b + 2 a)^{2} (x - y)

共通項をくくり出す

(- b + 2 a) (x - y)

= (- b + 2 a) (x - y) (4 (x - y) - 27 (- b + 2 a)^{2})