If $a, b$ are transcendental then $a+b$ is transcendental or $ab$ is transcendental

Question

I have to prove the following:

If $a, b$ are transcendental then $a+b$ is transcendental or $ab$ is transcendental, or both.

I don't have any idea on how to solve this. I already proved this:

If $z \in \mathbb{C}$, $a_1, a_2$ are algebraic then:
$z^2 + a_1z +a_2 = 0$ $\Rightarrow$ $z$ is algebraic

But I don't know if this could help me. Could you help me with this problem?

Thanks in advance