因数 x^3y^6-8w^3

解

因数

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

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

解答ステップ

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

x^{3} y^{6}

を書き換え

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

8 w^{3}

を書き換え

(2 w)^{3}

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

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

簡素化

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

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