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Evaluate each of the following using identities:$(2x -\frac{1}{x})^2$
Given:
$(2x -\frac{1}{2}x)^2$
To do:
We have to evaluate the given expression using a suitable identity.
Solution:
We know that,
$(a+b)^2=a^2+b^2+2ab$
$(a-b)^2=a^2+b^2-2ab$
$(a+b)(a-b)=a^2-b^2$
Therefore,
$(2 x-\frac{1}{x})^{2}=(2 x)^{2}+(\frac{1}{x})^{2}-2 \times 2 x \times \frac{1}{x}$
$=4 x^{2}-4+\frac{1}{x^{2}}$
Hence, $(2 x-\frac{1}{x})^{2}=4 x^{2}-4+\frac{1}{x^{2}}$.
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