展開する ((x^2+y^2)^{1/2}+3y)^2

解

展開する

((x^{2} + y^{2})^{\frac{1}{2}} + 3 y)^{2}

x^{2} + 10 y^{2} + 6 y (x^{2} + y^{2})^{\frac{1}{2}}

解答ステップ

((x^{2} + y^{2})^{\frac{1}{2}} + 3 y)^{2}

完全平方式を適用する:

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

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

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

簡素化

((x^{2} + y^{2})^{\frac{1}{2}})^{2} + 2 (x^{2} + y^{2})^{\frac{1}{2}} \cdot 3 y + (3 y)^{2} : x^{2} + 10 y^{2} + 6 y (x^{2} + y^{2})^{\frac{1}{2}}

= x^{2} + 10 y^{2} + 6 y (x^{2} + y^{2})^{\frac{1}{2}}