[Maths] - Algebra

Can someone explain to me what was done in the picture below?

A factor of $\frac{n(n+1)}{4}$ has been pulled out.

A factor of $\frac{n(n+1)}{4}$ has been pulled out.

Am i suppose to be able to spot factors like that because i dont usually check for factors first, I think that is a bad habit, If I attempted that, which I did first thing I would of done was take a factor of n/4 then expand the terms inside the big bracket. Im guessing that would give me the correct answer but not in the form the book wants it

You could do that, but it's easier to factorise as you don't have to deal with high degrees of n. Factorise everything that is common. When I'm doing a question like that I carefully consider each factor and see if they are common, if they are, then factorise it out.