# Math Help - simple algebra question

1. ## simple algebra question

Hi

Shame on me for asking this but

$\bigg(\frac{(n+1)(n+2)}{2}\bigg)^2 - \bigg(\frac{n(n+1)}{2}\bigg)^2$

Do you multiply everything out before subtracting ?
I got the answer n+1 but it's wrong.

2. Hello Jones
Originally Posted by Jones
Hi

Shame on me for asking this but

$\bigg(\frac{(n+1)(n+2)}{2}\bigg)^2 - \bigg(\frac{n(n+1)}{2}\bigg)^2$

Do you multiply everything out before subtracting ?
I got the answer n+1 but it's wrong.
No, not if you want the easiest method!

Note that each term has a common factor $\frac{n+1}{2}$, so take it out (not forgetting that it has to be squared):

$\bigg(\frac{(n+1)(n+2)}{2}\bigg)^2 - \bigg(\frac{n(n+1)}{2}\bigg)^2= \Big(\frac{n+1}{2}\Big)^2\Big((n+2)^2-n^2\Big)$

Even now, there's no need to multiply out. Use 'difference of two squares' in the second bracket.