Factoring 3(n+r)(n+r-1) + (n+r)

[confused88]

Can someone please help me with very simple math.. and explain slowly how they got from
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]

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]

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.

 

[confused88]

Oh wow i get it now. Thank you!