Factorize: `a^3-1/a^3-2a+2/a`

Explanation

Substituting `1/a` as `b`
`a^3-b^3-2a+2b`
Taking first term `a^3-b^3=(a-b)(a^2+ab+b^2)`
Second term `=-2(a-b)`
Now, putting values in equation, we have `(a-b) (a^2+ab+b^2)-2(a-b)`
`:.a-b` is common
So ,`(a-b) ((a^2+ab+b^2)-2(1))`
Substituting `b =1/a`
`(a-1/a)(a^2+axx1/a+1/a^2-2)`
`(a-1/a)(a^2+1/a^2+1-2)`
`(a-1/a) (a^2+1/a^2-1)`