展開する (4x^{2/3}+1)^2

解

展開する

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

16 x^{\frac{4}{3}} + 8 x^{\frac{2}{3}} + 1

解答ステップ

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

完全平方式を適用する:

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

(4 x^{\frac{2}{3}} + 1)^{2} = (4 x^{\frac{2}{3}})^{2} + 2 \cdot 4 x^{\frac{2}{3}} \cdot 1 + 1^{2}

= (4 x^{\frac{2}{3}})^{2} + 2 \cdot 4 x^{\frac{2}{3}} \cdot 1 + 1^{2}

(4 x^{\frac{2}{3}})^{2} = 16 x^{\frac{4}{3}}

2 \cdot 4 x^{\frac{2}{3}} \cdot 1 = 8 x^{\frac{2}{3}}

1^{2} = 1

= 16 x^{\frac{4}{3}} + 8 x^{\frac{2}{3}} + 1