因数 27x^6-125y^6

解

因数

27 x^{6} - 125 y^{6}

(3 x^{2} - 5 y^{2}) (9 x^{4} + 15 x^{2} y^{2} + 25 y^{4})

解答ステップ

27 x^{6} - 125 y^{6}

指数の規則を適用する

= (3 x^{2})^{3} - (5 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})

(3 x^{2})^{3} - (5 y^{2})^{3} = (3 x^{2} - 5 y^{2}) ((3 x^{2})^{2} + 3 x^{2} \cdot 5 y^{2} + (5 y^{2})^{2})

= (3 x^{2} - 5 y^{2}) ((3 x^{2})^{2} + 3 x^{2} \cdot 5 y^{2} + (5 y^{2})^{2})

簡素化

(3 x^{2})^{2} + 3 x^{2} \cdot 5 y^{2} + (5 y^{2})^{2} : 9 x^{4} + 15 x^{2} y^{2} + 25 y^{4}

= (3 x^{2} - 5 y^{2}) (9 x^{4} + 15 x^{2} y^{2} + 25 y^{4})