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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Updated on: 10-Oct-2022

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