因数 8x^6-27y^9

解

因数

8 x^{6} - 27 y^{9}

(2 x^{2} - 3 y^{3}) (4 x^{4} + 6 x^{2} y^{3} + 9 y^{6})

解答ステップ

8 x^{6} - 27 y^{9}

指数の規則を適用する

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

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

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

簡素化

(2 x^{2})^{2} + 2 x^{2} \cdot 3 y^{3} + (3 y^{3})^{2} : 4 x^{4} + 6 x^{2} y^{3} + 9 y^{6}

= (2 x^{2} - 3 y^{3}) (4 x^{4} + 6 x^{2} y^{3} + 9 y^{6})