展開する (L^{1/3}+K^{1/3})^3

解

展開する

(L^{\frac{1}{3}} + K^{\frac{1}{3}})^{3}

L + 3 L^{\frac{2}{3}} K^{\frac{1}{3}} + 3 L^{\frac{1}{3}} K^{\frac{2}{3}} + K

解答ステップ

(L^{\frac{1}{3}} + K^{\frac{1}{3}})^{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}

(L^{\frac{1}{3}} + K^{\frac{1}{3}})^{3} = (L^{\frac{1}{3}})^{3} + 3 (L^{\frac{1}{3}})^{2} K^{\frac{1}{3}} + 3 L^{\frac{1}{3}} (K^{\frac{1}{3}})^{2} + (K^{\frac{1}{3}})^{3}

= (L^{\frac{1}{3}})^{3} + 3 (L^{\frac{1}{3}})^{2} K^{\frac{1}{3}} + 3 L^{\frac{1}{3}} (K^{\frac{1}{3}})^{2} + (K^{\frac{1}{3}})^{3}

(L^{\frac{1}{3}})^{3} = L

(L^{\frac{1}{3}})^{2} = L^{\frac{2}{3}}

(K^{\frac{1}{3}})^{2} = K^{\frac{2}{3}}

(K^{\frac{1}{3}})^{3} = K

= L + 3 L^{\frac{2}{3}} K^{\frac{1}{3}} + 3 L^{\frac{1}{3}} K^{\frac{2}{3}} + K