# Expand and factorise

3(n+r)(n+r-1) + (n+r)
to (n+r)(3n+3r-2)?

I forgot how to factorise, so can someone help me do this please?

CRGreathouse
Homework Helper
The n+r is already factored out. Just write everything in terms of that and you'll see.

(It's actually easier to understand by doing, in this case, than to have it explained!)

Mentallic
Homework Helper
Explain slowly you say? Maybe that can be expressed through example.

ab+ac=a(b+c)
xy+x=x(y+1)
pqr+r=r(pq+1)

If you understand how to do the opposite of factorising which is expanding, then these results would be easy to confirm.

So for 3(n+r)(n+r-1) + (n+r)
let n+r=x
So we now have 3x(x-1)+x
Factorising x out: x(3(x-1)+1)
Expand 3(x-1) and collect like terms, then substitute n+r=x back into the result.

Oh wow i get it now. Thank you!!