Add or Subtract. Please explain how to do the process so I can understand it!!

7a^2 - 10a^2 + 9a

Question

Add or Subtract. Please explain how to do the process so I can understand it!!

7a^2 - 10a^2 + 9a

accessdenied · Answer

Do you understand the process of distributing?  Like, a(b + c) = ab + ac?
What I would like to propose for understanding this problem is factoring, which is the reverse process of distributing.  (ab + ac = a(b+c))

anonymous · Answer

I sort of understand it, it's been a while since I've done it.

accessdenied · Answer

Would it make sense if I said that a^2* (7-10) = 7a^2 - 10a^2 then?

anonymous · Answer

No not really, sorry lol, i'm really not that great at polynomials and monomials...

accessdenied · Answer

If we can agree that these are the same thing, then we can say that
  7a^2 - 10a^2 = a^2 * (7-10), or (7 - 10)a^2

7a^2 - 10a^2 + 9a = (7 - 10)a^2 + 9a

anonymous · Answer

oh! I get that now.

accessdenied · Answer

|dw:1359939505516:dw|
I think that's the best way to illustrate how adding/subtracting like-terms works out.  If they have the same variable and exponent, then it may be factored out and all that remains are the #'s in front of them.

If we tried to add 10a^2 + 9a, factoring = (10a + 9)a, we can't pull out another a to add anything so it fails.  :)