Question

Find the product:

$\left(x^4+\frac{1}{x^4}\right)\left(x+\frac{1}{x}\right)$

Answer 1

$$\begin{gathered} \left({\mathrm{x}}^4+\frac{1}{{\mathrm{x}}^4}\right)(\mathrm{x}+\frac{1}{\mathrm{x}}) \\ ={\mathrm{x}}^4\times (\mathrm{x}+\frac{1}{\mathrm{x}})+\frac{1}{{\mathrm{x}}^4}\times (\mathrm{x}+\frac{1}{\mathrm{x}}) \\ =({\mathrm{x}}^4\times \mathrm{x}+{\mathrm{x}}^4\times \frac{1}{\mathrm{x}})+(\frac{1}{{\mathrm{x}}^4}\times \mathrm{x}+\frac{1}{{\mathrm{x}}^4}\times \frac{1}{\mathrm{x}}) \\ ={\mathrm{x}}^5+{\mathrm{x}}^3+\frac{1}{{\mathrm{x}}^3}+\frac{1}{{\mathrm{x}}^5} \end{gathered}$$