展開する (3m^4-4m^3n)^3

解

展開する

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

27 m^{12} - 108 m^{11} n + 144 m^{10} n^{2} - 64 m^{9} n^{3}

解答ステップ

(3 m^{4} - 4 m^{3} 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}

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

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

簡素化

(3 m^{4})^{3} - 3 (3 m^{4})^{2} \cdot 4 m^{3} n + 3 \cdot 3 m^{4} (4 m^{3} n)^{2} - (4 m^{3} n)^{3} : 27 m^{12} - 108 m^{11} n + 144 m^{10} n^{2} - 64 m^{9} n^{3}

= 27 m^{12} - 108 m^{11} n + 144 m^{10} n^{2} - 64 m^{9} n^{3}