Question:
Find the product:
$\left(x^{4}+\frac{1}{x^{4}}\right) \times\left(x+\frac{1}{x}\right)$
Solution:
By horizontal method:
$\left(x^{4}+\frac{1}{x^{4}}\right) \times\left(x+\frac{1}{x}\right)$
$=x^{4}\left(x+\frac{1}{x}\right)+\frac{1}{x^{4}}\left(x+\frac{1}{x}\right)$
$=x^{5}+x^{3}+\frac{1}{x^{3}}+\frac{1}{x^{5}}$
i. e $x^{3}\left(x^{2}+1\right)+\frac{1}{x^{3}}\left(1+\frac{1}{x^{2}}\right)$