Let $X$ be a random variable that is $X \sim \mathrm{Unif}(0,1) = 1$. Use a transformation method to find the pdf of $U = X(1 - X)$.
I tried solving for $X$ and I got $X = \dfrac{1 \pm \sqrt{1-4U}}{2}$
But the actual pdf is $\dfrac{2}{\sqrt{1-4U}}$, so I can't just take $X'$