展開する (a^{9/2}-b^{9/2})^2

解

展開する

(a^{\frac{9}{2}} - b^{\frac{9}{2}})^{2}

a^{9} - 2 a^{\frac{9}{2}} b^{\frac{9}{2}} + b^{9}

解答ステップ

(a^{\frac{9}{2}} - b^{\frac{9}{2}})^{2}

完全平方式を適用する:

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

(a^{\frac{9}{2}} - b^{\frac{9}{2}})^{2} = (a^{\frac{9}{2}})^{2} - 2 a^{\frac{9}{2}} b^{\frac{9}{2}} + (b^{\frac{9}{2}})^{2}

= (a^{\frac{9}{2}})^{2} - 2 a^{\frac{9}{2}} b^{\frac{9}{2}} + (b^{\frac{9}{2}})^{2}

(a^{\frac{9}{2}})^{2} = a^{9}

(b^{\frac{9}{2}})^{2} = b^{9}

= a^{9} - 2 a^{\frac{9}{2}} b^{\frac{9}{2}} + b^{9}