展開する (2x^{2/3}+3)^2

解

展開する

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

4 x^{\frac{4}{3}} + 12 x^{\frac{2}{3}} + 9

解答ステップ

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

完全平方式を適用する:

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

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

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

(2 x^{\frac{2}{3}})^{2} = 4 x^{\frac{4}{3}}

2 \cdot 2 x^{\frac{2}{3}} \cdot 3 = 12 x^{\frac{2}{3}}

3^{2} = 9

= 4 x^{\frac{4}{3}} + 12 x^{\frac{2}{3}} + 9