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Multiplication of Any Polynomial

simplify: x...

Question

simplify: $(x^{3} + \frac{1}{x^{3}}) (x^{3} - \frac{1}{x^{3}})$

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Solution

$(x^{3} + (\frac{1}{x^{3}})) (x^{3} - (\frac{1}{x^{3}})) u s e (a + b) (a - b) = a^{2} - b^{2} ∴ v a l u e = (x^{3})^{2} - (x (\frac{1}{x^{3}})^{2}) = x^{6} - (\frac{1}{x^{6}})$

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(x^{3} - \frac{1}{x^{3}}) (x^{3} + \frac{1}{x^{3}}) (x^{6} + \frac{1}{x^{6}}) = (x^{12} - \frac{1}{x^{12}})

Q. Find the product of the following binomials:

(x^{3} + \frac{1}{x^{3}}) (x^{3} - \frac{1}{x^{3}})

\frac{1}{x + p} + \frac{1}{x + q} + \frac{1}{x + r} + \frac{p x}{x^{3} + p x^{2}} + \frac{q x}{x^{3} + p x^{2}} + \frac{r x}{x^{3} + r x}

\frac{{(\frac{1}{x})}^{- 1}}{{(\frac{1}{x})}^{3}}

{(\sqrt{x} + \frac{1}{\sqrt{x}})}^{3}

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