展開する (m^4+1/5 n)^3

解

展開する

(m^{4} + \frac{1}{5} n)^{3}

\frac{125 m ^{12} + 75 m ^{8} n + n ^{3} + 15 m ^{4} n ^{2}}{125}

解答ステップ

(m^{4} + \frac{1}{5} 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}

(m^{4} + \frac{1}{5} n)^{3} = (m^{4})^{3} + 3 (m^{4})^{2} \frac{1}{5} n + 3 m^{4} (\frac{1}{5} n)^{2} + (\frac{1}{5} n)^{3}

= (m^{4})^{3} + 3 (m^{4})^{2} \frac{1}{5} n + 3 m^{4} (\frac{1}{5} n)^{2} + (\frac{1}{5} n)^{3}

簡素化

(m^{4})^{3} + 3 (m^{4})^{2} \frac{1}{5} n + 3 m^{4} (\frac{1}{5} n)^{2} + (\frac{1}{5} n)^{3} : \frac{125 m ^{12} + 75 m ^{8} n + n ^{3} + 15 m ^{4} n ^{2}}{125}

= \frac{125 m ^{12} + 75 m ^{8} n + n ^{3} + 15 m ^{4} n ^{2}}{125}