因数 x^3y^6-64

解

因数

x^{3} y^{6} - 64

(x y^{2} - 4) (x^{2} y^{4} + 4 x y^{2} + 16)

解答ステップ

x^{3} y^{6} - 64

指数の規則を適用する

= (x y^{2})^{3} - 4^{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} - 4^{3} = (x y^{2} - 4) ((x y^{2})^{2} + 4 x y^{2} + 4^{2})

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

簡素化

(x y^{2})^{2} + 4 x y^{2} + 4^{2} : x^{2} y^{4} + 4 x y^{2} + 16

= (x y^{2} - 4) (x^{2} y^{4} + 4 x y^{2} + 16)