Expand: ${∣ ∣ ∣ \frac{1}{a} - \frac{1}{2 b} + 1 ∣ ∣ ∣}^{2}$

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Solution

$| \frac{1}{a} - \frac{1}{2 b} + 1 |^{2} = \frac{1}{a^{2}} + \frac{1}{4 b^{2}} + 1 - \frac{1}{a b} - \frac{1}{b} + \frac{2}{a}$

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Expand the following, using suitable identities: ${(\frac{1}{4} a - \frac{1}{2} b + 1)}^{2}$ [3 MARKS]

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