因数 64x^6-y^9

解

因数

64 x^{6} - y^{9}

(4 x^{2} - y^{3}) (16 x^{4} + 4 x^{2} y^{3} + y^{6})

解答ステップ

64 x^{6} - y^{9}

指数の規則を適用する

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

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

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

簡素化

(4 x^{2})^{2} + 4 x^{2} y^{3} + (y^{3})^{2} : 16 x^{4} + 4 x^{2} y^{3} + y^{6}

= (4 x^{2} - y^{3}) (16 x^{4} + 4 x^{2} y^{3} + y^{6})