因数 9-(x-y)^2

解

因数

9 - (x - y)^{2}

(3 + x - y) (3 - x + y)

解答ステップ

9 - (x - y)^{2}

数を因数に分解する:

9 = 3^{2}

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

2乗の差の公式を適用する:

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

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

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

簡素化

(3 + (x - y)) (3 - (x - y)) : (3 + x - y) (3 - x + y)

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