Show that if R has no zero divisors, then R[x] has no zero divisors.

Since R has no zero divisors, then $\displaystyle \forall a,b\in R$ such that $\displaystyle a,b\neq 0$, $\displaystyle ab\neq 0$.

Is this next part correct (not sure what to do next)?

$\displaystyle R[ab]=R[a]R[b]\neq 0$