What is expand (1/2+(2a^2)/b)^2 ?

The solution to expand (1/2+(2a^2)/b)^2 is (b^2+8a^2b+16a^4)/(4b^2)

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expand (1/2+(2a^2)/b)^2

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

(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}

Simplify

(\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}}

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What is expand (1/2+(2a^2)/b)^2 ?
The solution to expand (1/2+(2a^2)/b)^2 is (b^2+8a^2b+16a^4)/(4b^2)