因数 27u^3+8n^6m^9

解

因数

27 u^{3} + 8 n^{6} m^{9}

(3 u + 2 n^{2} m^{3}) (9 u^{2} - 6 n^{2} m^{3} u + 4 n^{4} m^{6})

解答ステップ

27 u^{3} + 8 n^{6} m^{9}

27 u^{3}

を書き換え

(3 u)^{3}

8 n^{6} m^{9}

を書き換え

(2 n^{2} m^{3})^{3}

= (3 u)^{3} + (2 n^{2} m^{3})^{3}

立方数の和の公式を適用する:

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

(3 u)^{3} + (2 n^{2} m^{3})^{3} = (3 u + 2 n^{2} m^{3}) ((3 u)^{2} - 2 n^{2} m^{3} 3 u + (2 n^{2} m^{3})^{2})

= (2 n^{2} m^{3} + 3 u) ((2 n^{2} m^{3})^{2} - 2 n^{2} m^{3} 3 u + (3 u)^{2})

簡素化

(3 u + 2 n^{2} m^{3}) ((3 u)^{2} - 2 n^{2} m^{3} \cdot 3 u + (2 n^{2} m^{3})^{2}) : (3 u + 2 n^{2} m^{3}) (9 u^{2} - 6 n^{2} m^{3} u + 4 n^{4} m^{6})

= (3 u + 2 n^{2} m^{3}) (9 u^{2} - 6 n^{2} m^{3} u + 4 n^{4} m^{6})