因数 x^4-100y^2

解

因数

x^{4} - 100 y^{2}

(x^{2} + 10 y) (x^{2} - 10 y)

解答ステップ

x^{4} - 100 y^{2}

x^{4} = (x^{2})^{2}

100 y^{2} = (10 y)^{2}

= (x^{2})^{2} - (10 y)^{2}

2乗の差の公式を適用する:

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

(x^{2})^{2} - (10 y)^{2} = (x^{2} + 10 y) (x^{2} - 10 y)

= (x^{2} + 10 y) (x^{2} - 10 y)