展開する (1-x^{2/3})^3

解

展開する

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

1 - 3 x^{\frac{2}{3}} + 3 x^{\frac{4}{3}} - x^{2}

解答ステップ

(1 - x^{\frac{2}{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}

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

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

1^{3} = 1

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

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

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

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