因数 x^6-8y^6

解

因数

x^{6} - 8 y^{6}

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

解答ステップ

x^{6} - 8 y^{6}

指数の規則を適用する

= (x^{2})^{3} - (2 y^{2})^{3}

立方数の差の公式を適用する:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

(x^{2})^{3} - (2 y^{2})^{3} = (x^{2} - 2 y^{2}) ((x^{2})^{2} + x^{2} \cdot 2 y^{2} + (2 y^{2})^{2})

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

簡素化

(x^{2})^{2} + x^{2} \cdot 2 y^{2} + (2 y^{2})^{2} : x^{4} + 2 x^{2} y^{2} + 4 y^{4}

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