因数 (5x+2y)^2-(3x-y)^2

解

因数

(5 x + 2 y)^{2} - (3 x - y)^{2}

(8 x + y) (2 x + 3 y)

解答ステップ

(5 x + 2 y)^{2} - (3 x - y)^{2}

2乗の差の公式を適用する:

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

(5 x + 2 y)^{2} - (3 x - y)^{2} = ((5 x + 2 y) + (3 x - y)) ((5 x + 2 y) - (3 x - y))

= ((5 x + 2 y) + (3 x - y)) ((5 x + 2 y) - (3 x - y))

簡素化

((5 x + 2 y) + (3 x - y)) ((5 x + 2 y) - (3 x - y)) : (8 x + y) (2 x + 3 y)

= (8 x + y) (2 x + 3 y)