I have this expression:
$$4n^2-n+(8(n+1)-5)$$
And I know it is equivalent to this:
$$4(n+1)^2-(n+1)$$
I need to simplify my expression to get the same structure as that one. However, no matter what I try, I don't end up with that structure.
My question is, well, how to reach that. But truly, the real problem is that I seem to lack this sense of "knowing which method to use to simplify to get the structure I want". Is there some kind of rule or guide about this? Or is it all about practice and experience?
Edit
If anyone was curious, I ended up with this: $$4n^2+7n+3$$ Yes, I did multiplications and additions. Couldn't find common factor (as far I can tell) or any other trick.