TITLE: Simple factoring in proof by induction
QUESTION [6 upvotes]: How would this:
$$\frac{((n+1)+1)(2(n+1) + 1)(2(n+1) + 3)}{3}$$
Factor to this:
$$(2(n+1)+1)^2$$
This is a part of an induction proof, which I would post an image if my reputation was higher... Writing this from a phone but will add more detail later if needed thanks again.
Thank you, please include all the steps-
EDIT
Thanks amWhy, must be something else happening in the proof... 

EDIT
Thanks anorton the LaTex helps, so below is the link to the proof, I'm still trying to understand the initial inductive steps in this method, let me know if more is needed:

REPLY [4 votes]: What you need to show instead is $$\frac{((n+1)+1)(2(n+1)+1)(2(n+1)+3)}{3}-\frac{(n+1)(2n+1)(2n+3)}{3}=(2(n+1)+1)^2$$