展開する (6mn^2-4n)^3

解

展開する

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

216 m^{3} n^{6} - 432 n^{5} m^{2} + 288 m n^{4} - 64 n^{3}

解答ステップ

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

完全立方式を適用する:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(6 m n^{2} - 4 n)^{3} = (6 m n^{2})^{3} - 3 (6 m n^{2})^{2} \cdot 4 n + 3 \cdot 6 m n^{2} (4 n)^{2} - (4 n)^{3}

= (6 m n^{2})^{3} - 3 (6 m n^{2})^{2} \cdot 4 n + 3 \cdot 6 m n^{2} (4 n)^{2} - (4 n)^{3}

簡素化

(6 m n^{2})^{3} - 3 (6 m n^{2})^{2} \cdot 4 n + 3 \cdot 6 m n^{2} (4 n)^{2} - (4 n)^{3} : 216 m^{3} n^{6} - 432 n^{5} m^{2} + 288 m n^{4} - 64 n^{3}

= 216 m^{3} n^{6} - 432 n^{5} m^{2} + 288 m n^{4} - 64 n^{3}