展開する (x^{1/3}+y^{1/3})^3

解

展開する

(x^{\frac{1}{3}} + y^{\frac{1}{3}})^{3}

x + 3 x^{\frac{2}{3}} y^{\frac{1}{3}} + 3 x^{\frac{1}{3}} y^{\frac{2}{3}} + y

解答ステップ

(x^{\frac{1}{3}} + y^{\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}

(x^{\frac{1}{3}} + y^{\frac{1}{3}})^{3} = (x^{\frac{1}{3}})^{3} + 3 (x^{\frac{1}{3}})^{2} y^{\frac{1}{3}} + 3 x^{\frac{1}{3}} (y^{\frac{1}{3}})^{2} + (y^{\frac{1}{3}})^{3}

= (x^{\frac{1}{3}})^{3} + 3 (x^{\frac{1}{3}})^{2} y^{\frac{1}{3}} + 3 x^{\frac{1}{3}} (y^{\frac{1}{3}})^{2} + (y^{\frac{1}{3}})^{3}

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

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

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

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

= x + 3 x^{\frac{2}{3}} y^{\frac{1}{3}} + 3 x^{\frac{1}{3}} y^{\frac{2}{3}} + y