Question:

Notice that the best first move is to reveal the hidden structure in the expression. A clever move here is to rewrite the problem in the form where the standard theorem or identity applies cleanly. If $a = x^{1/3}$, then $a^3 = x$ and $a^{-3} = 1/x$. The question as written in MFA008 uses a specific relation; after applying the cube identity the answer simplifies to $a^3 - 3a$. Now, we invoke the power of that idea, simplify patiently, and then check that the final answer really fits the original problem.