Question

Factorize $a^3-\frac{1}{a^3}-2a+\frac{2}{a}$

Answer 1

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