Subject: Pre-Algebra
Name: Jessica
Who are you: Student

11/6/06 5:30 pm
Dear tutor,
I am glad to have found your web sites, and to know that you're giving up your time to help others. When I began getting frustrated today because I didn't understand how to do a certain problem, I went to google and typed in-Simplifying Variable Expressions. When I did, I came to your web site and began reading other questions from other people and decided you were the exact help I was looking for. Finally, what I didn't understand about simplifying variable expressions was:

-21(a+2b)+14a-9b (this is only one of the many questions I wish you had time to answer).

I look forward to your response. Thank you!

Hi Jessica.

I hope you find this message, because we didn't get your right email address. Perhaps you are using our link to the latest Quandaries and Queries, though. That would find this article quickly enough.

You asked about simplifying -21(a+2b)+14a-9b.

The important thing to remember is that you can add apples to apples and oranges to oranges, but you can't add (or subtract) apples to oranges. In algebra, the types of fruit are the variable names like a and b in your expression.

I'm going to show you how to solve a slightly changed problem:

Simplify 4x - 9( y - 3x) - 8 + 10y.

First multiply through by -9 to remove the parentheses:

4x - 9y + 27x - 8 + 10y

Now group "like" terms. That means you can add the terms (the terms are the things between the pluses and minuses) together that have the same variables only. So 4x and - 27x are like terms. And -9y and 10y are like terms. So that means

(4x + 27x) + (-9y + 10y) - 8

which is

31x + y - 8.

Each of these three terms has no other "like" terms, so this is simplified.

You can solve your expression using the same steps I've shown you here.

Hope this helps,
Stephen La Rocque.