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### 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

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.

x - 5y + 2x + 3y

We separate them like this:

x, 2x    and   -5y,  3y

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/
```
Associated Topics:
Middle School Algebra

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