因数 16-(x+y)^2

解

因数

16 - (x + y)^{2}

(4 + x + y) (4 - x - y)

解答ステップ

16 - (x + y)^{2}

数を因数に分解する:

16 = 4^{2}

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

2乗の差の公式を適用する:

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

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

= (4 + (x + y)) (4 - (x + y))

簡素化

(4 + (x + y)) (4 - (x + y)) : (4 + x + y) (4 - x - y)

= (4 + x + y) (4 - x - y)