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Algebraic Identities

Use suitable ...

Question

Use suitable identities to find the product :
$(x^{2} + \frac{1}{x^{2}}) (x^{2} - \frac{1}{x^{2}})$

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Solution

We need to find value of $(x^{2} + \frac{1}{x^{2}}) (x^{2} - \frac{1}{x^{2}})$
The suitable identities $(x + y) (x - y) = x^{2} - y^{2}$
Therefore, value of $(x^{2} + \frac{1}{x^{2}}) (x^{2} - \frac{1}{x^{2}})$ is
$= ((x^{2})^{2} - \frac{1}{(x^{2})^{2}})$
$= x^{4} - \frac{1}{x^{4}}$

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