Factorize the following expression : \(a^3 – \frac{1}{a^3} – 2a + \frac{2}{a}\)

\[ a^3 – \frac{1}{a^3} – 2a + \frac{2}{a} \] \[ = \left(a^3 – \frac{1}{a^3}\right) – 2\left(a – \frac{1}{a}\right) \] \[ = \left(a – \frac{1}{a}\right)\left(a^2 + 1 + \frac{1}{a^2}\right) – 2\left(a – \frac{1}{a}\right) \] \[ = \left(a – \frac{1}{a}\right) \left(a^2 + 1 + \frac{1}{a^2} – 2\right) \] \[ = \left(a – \frac{1}{a}\right) \left(a^2 – 1 + \frac{1}{a^2}\right) \]