Simplifying Expressions

Date: 01/27/97 at 20:18:34
From: Emily McDaniel
Subject: Algebra/polynomials

The problem is 3x-2y-x-3y.  I tried to combine the same terms, but 
still am confused.

Date: 01/30/97 at 12:55:36
From: Doctor Wallace
Subject: Re: Algebra/polynomials

Hi Emily!

You're definitely on the right track here. You need to combine like 
terms.

The question is, which are the like terms? Well, you've heard the old 
saying "You can't add apples and oranges?" What? You haven't?  Well, 
anyway, you can't.

And you can't add x's and y's, either. So we need to separate them.

Let's separate the problem into terms. We have 4 of them:

           3x    -2y    -x    -3y

I just wrote out the problem, breaking it into terms.  A term is one 
little unit of the problem, consisting of a variable (x or y) and its 
coefficient (the number stuck next to it in front).

Note that we have to keep the minus signs with the proper terms.  The 
minus signs are always in front of a term, so when we break up the 
problem, we keep the minus signs with the terms immediately following 
the minus signs.

Okay, now we can put x's with x's and y's with y's.  So we rearrange 
like this:

          3x  -x      -2y  -3y


Now we add (or subtract, depending on how you look at it) each part:

            3x + (-x)     and    (-2y) + (-3y)

to get

               2x         and        -5y

Now we just write them together without the "and" or comma, and 
presto!  We have the answer:

                      2x - 5y

One note of explanation here.  When I said above "add or subtract, 
depending on how you look at it" I mean that:

   3x + (-x)  is the same thing as    (3x) - (x)
                 and
(-2y) + (-3y)  is the same thing as  (-2y) - (3y)


This is where it is easy to get confused.  The minus sign can mean 
either to ADD the negative of a number, or SUBTRACT the positive of 
the number.  You may use either, as long as you are consistent.

When you get used to this simplification method, you'll be able to do 
it just by looking at the problem.  

Let's try another. How about:

      x - 5y + 2x + 3y

We separate them like this:

       x, 2x    and   -5y,  3y
 
then add:

      x + 2x    and   -5y + 3y

to get: 3x      and   -2y


so our answer is:  3x - 2y  which is the same as  3x + (-2y)

Okay?  Thanks for writing!  If you have any more trouble, or need more 
help on this or any other math question, don't wait - write back!

-Doctor Wallace,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/