展開する (1/2+(2a^2)/b)^2

解

展開する

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

\frac{b ^{2} + 8 a ^{2} b + 16 a ^{4}}{4 b ^{2}}

解答ステップ

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

完全平方式を適用する:

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

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

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

簡素化

(\frac{1}{2})^{2} + 2 \cdot \frac{1}{2} \cdot \frac{2 a ^{2}}{b} + (\frac{2 a ^{2}}{b})^{2} : \frac{b ^{2} + 8 a ^{2} b + 16 a ^{4}}{4 b ^{2}}

= \frac{b ^{2} + 8 a ^{2} b + 16 a ^{4}}{4 b ^{2}}