因数 8x^3-y^6

解

因数

8 x^{3} - y^{6}

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

解答ステップ

8 x^{3} - y^{6}

指数の規則を適用する

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

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

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

簡素化

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

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