因数 64u^6-27w^6

解

因数

64 u^{6} - 27 w^{6}

(4 u^{2} - 3 w^{2}) (16 u^{4} + 12 u^{2} w^{2} + 9 w^{4})

解答ステップ

64 u^{6} - 27 w^{6}

指数の規則を適用する

= (4 u^{2})^{3} - (3 w^{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})

(4 u^{2})^{3} - (3 w^{2})^{3} = (4 u^{2} - 3 w^{2}) ((4 u^{2})^{2} + 4 u^{2} \cdot 3 w^{2} + (3 w^{2})^{2})

= (4 u^{2} - 3 w^{2}) ((4 u^{2})^{2} + 4 u^{2} \cdot 3 w^{2} + (3 w^{2})^{2})

簡素化

(4 u^{2})^{2} + 4 u^{2} \cdot 3 w^{2} + (3 w^{2})^{2} : 16 u^{4} + 12 u^{2} w^{2} + 9 w^{4}

= (4 u^{2} - 3 w^{2}) (16 u^{4} + 12 u^{2} w^{2} + 9 w^{4})