因数 16x^4-(y-2z)^2

解

因数

16 x^{4} - (y - 2 z)^{2}

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

解答ステップ

16 x^{4} - (y - 2 z)^{2}

簡素化

16 x^{4} : (4 x^{2})^{2}

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

2乗の差の公式を適用する:

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

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

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

簡素化

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

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