algebra precalculus - How to get the simplest form of this radical expression: $3sqrt[3]{2a} - 6sqrt[3]{2a}$.

How to get the simplest form of this radical expression:
$$3\sqrt[3]{2a} - 6\sqrt[3]{2a}$$

Here is my work:
$$3\sqrt[3]{2a} - 6\sqrt[3]{2a}$$
Since the radicands are the same, we just add the coefficients.
$$-3\sqrt[3]{2a} \sqrt[3]{2a}$$
Since everything is under the same index it becomes:
$$-3\sqrt[3]{2} \sqrt[3]{a}$$

Did I do this correctly, if not can anyone tell me what I should do?
Thanks :-).

Answer

Your middle step is incorrect, it should be $-3\sqrt[3]{2a}$ not $-3\sqrt[3]{2a}\sqrt[3]{2a}$. It should be $$3\sqrt[3]{2a} - 6\sqrt[3]{2a} = 3\times\sqrt[3]{2a} - 6\times\sqrt[3]{2a} = (3 - 6)\times\sqrt[3]{2a} = -3\times\sqrt[3]{2a} = -3\sqrt[3]{2a}.$$ I don't think $-3\sqrt[3]{2}\sqrt[3]{a}$ is any simpler than $-3\sqrt[3]{2a}$, but that's just my opinion.