因数 25-x^2-16y^2+8xy

解

因数

25 - x^{2} - 16 y^{2} + 8 x y

(5 + x - 4 y) (5 - x + 4 y)

解答ステップ

25 - x^{2} - 16 y^{2} + 8 x y

因数

- x^{2} - 16 y^{2} + 8 x y : - (x - 4 y)^{2}

= 25 - (x - 4 y)^{2}

数を因数に分解する:

25 = 5^{2}

= 5^{2} - (x - 4 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 - 4 y)^{2} = (5 + (x - 4 y)) (5 - (x - 4 y))

= (5 + (x - 4 y)) (5 - (x - 4 y))

簡素化

(5 + (x - 4 y)) (5 - (x - 4 y)) : (5 + x - 4 y) (5 - x + 4 y)

= (5 + x - 4 y) (5 - x + 4 y)