展開する (3m-2n^2)^3

解

展開する

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

27 m^{3} - 54 m^{2} n^{2} + 36 m n^{4} - 8 n^{6}

解答ステップ

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

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

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

簡素化

(3 m)^{3} - 3 (3 m)^{2} \cdot 2 n^{2} + 3 \cdot 3 m (2 n^{2})^{2} - (2 n^{2})^{3} : 27 m^{3} - 54 m^{2} n^{2} + 36 m n^{4} - 8 n^{6}

= 27 m^{3} - 54 m^{2} n^{2} + 36 m n^{4} - 8 n^{6}