<s>[INST] Factoring $4x^{4} - x^{2}$ into $4x^{2}(x-1/2)(x+1/2)$ So i was trying to make an integral but i'm stuck with the easiest part.

How do you get this?
$$4x^{4} - x^{2} = 4x^{2}(x-1/2)(x+1/2)$$

I know how to take the roots $x = 0$, $x = \pm 1/2$,
but when putting it all together I get
$$x(x−1/2)(x+1/2)$$ and I can't remember how to do it correctly.
 [/INST] I think you meant $4x^{4} - x^{2}$. In such case, you can factor $x^{2}$ out and apply the following identity:
\begin{align*}
a^{2} - b^{2} = (a+b)(a-b)
\end{align*}
At your case, you have $4x^{4} - x^{2} = x^{2}(4x^{2} - 1)$, where $a = 2x$ and $b = 1$. Consequently, we get that
\begin{align*}
4x^{4} - x^{2} = x^{2}(2x-1)(2x+1) = 4x^{2}(x-1/2)(x+1/2)
\end{align*}
</s>