Question
Find the following products:
$\Big(\text{x}^4+\frac{1}{\text{x}^4})×\Big(\text{x}+\frac{1}{\text{x}}\Big)$
$\Big(\text{x}^4+\frac{1}{\text{x}^4})×\Big(\text{x}+\frac{1}{\text{x}}\Big)$
✓
Answer
$\Big(\text{x}^4+\frac{1}{\text{x}^4})×\Big(\text{x}+\frac{1}{\text{x}}\Big)$$=\text{x}^4\Big(\text{x}+\frac{1}{\text{x}}\Big)+\frac{1}{\text{x}^4}\Big(\text{x}+\frac{1}{\text{x}}\Big)$
$=\text{x}^4\times\text{x}+\frac{1}{\text{x}}+\frac{1}{\text{x}^4}\times\text{x}+\frac{1}{\text{x}^4}\times\frac{1}{\text{x}}$
$=\text{x}^5+\text{x}^3+\frac{1}{\text{x}^3}+\frac{1}{\text{x}^5}$
$=\text{x}^4\times\text{x}+\frac{1}{\text{x}}+\frac{1}{\text{x}^4}\times\text{x}+\frac{1}{\text{x}^4}\times\frac{1}{\text{x}}$
$=\text{x}^5+\text{x}^3+\frac{1}{\text{x}^3}+\frac{1}{\text{x}^5}$
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