real analysis - Show Uniform Convergence of $f_n(x)=n^2x^n(1-x)^2$

$f_n(x)=n^2x^n(1-x)^2$ on $[0,a]$ where $a<1$

I know that $f_n(x)$ converges to $f=0$

Uniformly converge iff:
for all $\epsilon >0$ there exists $n>N$ s.t.
$|f_n-f|<\epsilon$

So I should show that I can find $n$ such that

$|f_n-f|=|n^2x^n(1-x)^2-0|<\epsilon$ for all $0\leq x \leq a$

I already showed that it is not uniformly convergent on [0,1] by taking $f_n(1-1/n)$ because $(1-1/n)^n$ is 1 as $n \rightarrow \infty$

Answer

It is bounded on $[0,a]$ by $n^2a^n$, which converges to $0$ without depending on $x$.