展開する (x^{1/3}+3)^2

解

展開する

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

x^{\frac{2}{3}} + 6 x^{\frac{1}{3}} + 9

解答ステップ

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

完全平方式を適用する:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

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

2 x^{\frac{1}{3}} \cdot 3 = 6 x^{\frac{1}{3}}

3^{2} = 9

= x^{\frac{2}{3}} + 6 x^{\frac{1}{3}} + 9