展開する (ae_{0}^2+abe_{0}^3)^3

解

展開する

(a e_{0}^{2} + ab e_{0}^{3})^{3}

e^{6} a^{3} + 3 e^{7} a^{3} b + 3 e^{8} a^{3} b^{2} + e^{9} a^{3} b^{3}

解答ステップ

(a e_{0}^{2} + ab e_{0}^{3})^{3}

= (e_{0}^{2} a + e_{0}^{3} ab)^{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}

a = a e_{0}^{2}, b = ab e_{0}^{3}

= (a e_{0}^{2})^{3} + 3 (a e_{0}^{2})^{2} ab e_{0}^{3} + 3 a e_{0}^{2} (ab e_{0}^{3})^{2} + (ab e_{0}^{3})^{3}

簡素化

(a e_{0}^{2})^{3} + 3 (a e_{0}^{2})^{2} ab e_{0}^{3} + 3 a e_{0}^{2} (ab e_{0}^{3})^{2} + (ab e_{0}^{3})^{3} : e^{6} a^{3} + 3 e^{7} a^{3} b + 3 e^{8} a^{3} b^{2} + e^{9} a^{3} b^{3}

= e^{6} a^{3} + 3 e^{7} a^{3} b + 3 e^{8} a^{3} b^{2} + e^{9} a^{3} b^{3}