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Middle Terms

Expand 2x - 1...

Question

Expand ${(2 x - \frac{1}{2 x})}^{2}$

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Solution

Step 1: Applying the formula of the square of the difference of two terms:
${(2 x - \frac{1}{2 x})}^{2} = (2 x)^{2} - 2 \times (2 x) \times \frac{1}{(2 x)} + {(\frac{1}{2 x})}^{2}$
$[∵ (a - b)^{2} = a^{2} + b^{2} - 2 a b)$
$= 4 x^{2} - 2 + \frac{1}{4 x^{2}}$
Hence,
${(2 x - \frac{1}{2 x})}^{2} = 4 x^{2} - 2 + \frac{1}{4 x^{2}}$

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