Question

Solve : $(x^4+\frac{1}{x^4})\times (x+\frac{1}{x})$

Answer 1

Let us multiply the given binomials $(x^4+\frac{1}{x^4})$ and $(x+\frac{1}{x})$ as shown below:

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

Hence, $(x^4+\frac{1}{x^4})\times (x+\frac{1}{x})=x^5+x^3+\frac{1}{x^3}+\frac{1}{x^5}$.