展開する (2x^{1/2}-3z^{2/3})^3

解

展開する

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

8 x^{\frac{3}{2}} - 36 x z^{\frac{2}{3}} + 54 x^{\frac{1}{2}} z^{\frac{4}{3}} - 27 z^{2}

解答ステップ

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

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

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

(2 x^{\frac{1}{2}})^{3} = 8 x^{\frac{3}{2}}

3 (2 x^{\frac{1}{2}})^{2} \cdot 3 z^{\frac{2}{3}} = 36 x z^{\frac{2}{3}}

3 \cdot 2 x^{\frac{1}{2}} (3 z^{\frac{2}{3}})^{2} = 54 x^{\frac{1}{2}} z^{\frac{4}{3}}

(3 z^{\frac{2}{3}})^{3} = 27 z^{2}

= 8 x^{\frac{3}{2}} - 36 x z^{\frac{2}{3}} + 54 x^{\frac{1}{2}} z^{\frac{4}{3}} - 27 z^{2}