因数 (ax-3b)^2-(bx-3a)^2

解

因数

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

(a x - 3 a - 3 b + b x) (a x + 3 a - 3 b - b x)

解答ステップ

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

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

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

= ((a x - 3 b) + (b x - 3 a)) ((a x - 3 b) - (b x - 3 a))

簡素化

((a x - 3 b) + (b x - 3 a)) ((a x - 3 b) - (b x - 3 a)) : (a x - 3 b + b x - 3 a) (a x - 3 b - b x + 3 a)

= (a x - 3 b + b x - 3 a) (a x - 3 b - b x + 3 a)

= (a x - 3 a - 3 b + b x) (a x + 3 a - 3 b - b x)