展開する (a^{1/2}+b^{1/2})^2

解

展開する

(a^{\frac{1}{2}} + b^{\frac{1}{2}})^{2}

a + 2 a^{\frac{1}{2}} b^{\frac{1}{2}} + b

解答ステップ

(a^{\frac{1}{2}} + b^{\frac{1}{2}})^{2}

完全平方式を適用する:

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

(a^{\frac{1}{2}} + b^{\frac{1}{2}})^{2} = (a^{\frac{1}{2}})^{2} + 2 a^{\frac{1}{2}} b^{\frac{1}{2}} + (b^{\frac{1}{2}})^{2}

= (a^{\frac{1}{2}})^{2} + 2 a^{\frac{1}{2}} b^{\frac{1}{2}} + (b^{\frac{1}{2}})^{2}

(a^{\frac{1}{2}})^{2} = a

(b^{\frac{1}{2}})^{2} = b

= a + 2 a^{\frac{1}{2}} b^{\frac{1}{2}} + b