展開する (a^{3/5}-b^{3/5})^2

解

展開する

(a^{\frac{3}{5}} - b^{\frac{3}{5}})^{2}

a^{\frac{6}{5}} - 2 a^{\frac{3}{5}} b^{\frac{3}{5}} + b^{\frac{6}{5}}

解答ステップ

(a^{\frac{3}{5}} - b^{\frac{3}{5}})^{2}

完全平方式を適用する:

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

(a^{\frac{3}{5}} - b^{\frac{3}{5}})^{2} = (a^{\frac{3}{5}})^{2} - 2 a^{\frac{3}{5}} b^{\frac{3}{5}} + (b^{\frac{3}{5}})^{2}

= (a^{\frac{3}{5}})^{2} - 2 a^{\frac{3}{5}} b^{\frac{3}{5}} + (b^{\frac{3}{5}})^{2}

(a^{\frac{3}{5}})^{2} = a^{\frac{6}{5}}

(b^{\frac{3}{5}})^{2} = b^{\frac{6}{5}}

= a^{\frac{6}{5}} - 2 a^{\frac{3}{5}} b^{\frac{3}{5}} + b^{\frac{6}{5}}