Explaining an algebra step in $ \frac{n^2(n+1)^2}{4} + (n+1)^3 = \frac{(n+1)^2}{4}(n^2+4n+4)$ I have encountered this step in my textbook and I do not understand it, could someone please list the intermediate steps?
$$ \frac{n^2(n+1)^2}{4} + (n+1)^3 = \frac{(n+1)^2}{4}(n^2+4n+4). $$
Thanks, 

One way to see it is to factor out the $(n+1)^2/4$. Then
$$
\begin{align*}
\frac{n^2(n+1)^2}{4} + (n+1)^3 &=\frac{(n+1)^2}{4}\bigl(n^2+4(n+1)\bigr) \\
&= \frac{(n+1)^2}{4}(n^2+4n+4)
\end{align*}
$$
Since you factor out a $1/4$, you have to keep a $4$ in the numerator in the second term.
