因数 27m^{12}-64n^9

解

因数

27 m^{12} - 64 n^{9}

(3 m^{4} - 4 n^{3}) (9 m^{8} + 12 m^{4} n^{3} + 16 n^{6})

解答ステップ

27 m^{12} - 64 n^{9}

指数の規則を適用する

= (3 m^{4})^{3} - (4 n^{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})

(3 m^{4})^{3} - (4 n^{3})^{3} = (3 m^{4} - 4 n^{3}) ((3 m^{4})^{2} + 3 m^{4} \cdot 4 n^{3} + (4 n^{3})^{2})

= (3 m^{4} - 4 n^{3}) ((3 m^{4})^{2} + 3 m^{4} \cdot 4 n^{3} + (4 n^{3})^{2})

簡素化

(3 m^{4})^{2} + 3 m^{4} \cdot 4 n^{3} + (4 n^{3})^{2} : 9 m^{8} + 12 m^{4} n^{3} + 16 n^{6}

= (3 m^{4} - 4 n^{3}) (9 m^{8} + 12 m^{4} n^{3} + 16 n^{6})