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Multiplication of Any Polynomial

Expand: n - ...

Question

Expand: $(n - \frac{1}{n}) (n + \frac{1}{n}) (n^{2} + \frac{1}{n^{2}})$

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Solution

As we know the formula $(a + b) (a - b)$ = $a^{2} - b^{2}$
So $(n - \frac{1}{n}) (n + \frac{1}{n})$ = $(n)^{2} - (\frac{1}{n})^{2}$
= $(n)^{2} - (\frac{1}{n^{2}})$
= $(n^{2} - \frac{1}{n^{2}})$ $(n^{2} - \frac{1}{n^{2}})$
= $(n^{2} - \frac{1}{n^{2}})$ $(n^{2} - \frac{1}{n^{2}})$ = $(n^{2})^{2} - (\frac{1}{n^{2}})^{2}$
= $n^{4} - \frac{1}{n^{4}}$

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