因数 x^8-y^4

解

因数

x^{8} - y^{4}

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

解答ステップ

x^{8} - y^{4}

x^{8} = (x^{4})^{2}

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

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

2乗の差の公式を適用する:

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

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

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

因数

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

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