Find the product:

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 $x^{3}\left(x^{2}+1\right)+\frac{1}{x^{3}}\left(1+\frac{1}{x^{2}}\right)$

 

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