因数 25-(x-y)^2

解

因数

25 - (x - y)^{2}

(5 + x - y) (5 - x + y)

解答ステップ

25 - (x - y)^{2}

数を因数に分解する:

25 = 5^{2}

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

2乗の差の公式を適用する:

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

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

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

簡素化

(5 + (x - y)) (5 - (x - y)) : (5 + x - y) (5 - x + y)

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