​ Factorize each of the following expressions: a^3 - 1/(a^3) - 2a + 2/a

Question

Factorize each of the following expressions:

a³ - \(\frac{1}{a^3}\) - 2a + \(\frac{2}{a}\) 

Answer 1

Given,

\(a^{3}-\frac{1}{a^{3}}-2a+\frac{2}{a}\)

= \(a^{3}-\frac{1}{a^{3}}-2(a-\frac{1}{a})\)

= \((a-\frac{1}{a})(a^{2}+\frac{1}{a^{2}}+1)-2(a-\frac{1}{a})\)

= \((a-\frac{1}{a})(a^{2}+\frac{1}{a^{2}}+1-2)\)

= \((a-\frac{1}{a})(a^{2}+\frac{1}{a^2}-1)\)