Simplify the following:

$\Big(x + \dfrac{1}{x}\Big)\Big(x^2 - 1 + \dfrac{1}{x^2}\Big)$

We know that (a + b)(a² - ab + b²) = a³ + b³

∴ Given Expression = $\Big(x + \dfrac{1}{x}\Big)\Big(x^2 - 1 + \dfrac{1}{x^2}\Big)$

$= x^3 + \dfrac{1}{x^3}$