simple algebra question

**Jones** · October 6th 2009, 03:14 AM

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.

**Grandad** · October 6th 2009, 03:27 AM

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.

Grandad

**Jones** · October 6th 2009, 04:35 AM

Of curse!
Stupid me.

Thank you daddy!

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