How to Simplify Variable Expressions

When you enter algebra class, does the thought of working with x’s and y’s make you nervous? Do you find variables and variable expressions to be confusing? If you do, you are not alone. Many students find working with variables to be a challenge. One of the first things you will need to learn to do when working with variables is simplifying variable expressions. This is not a difficult concept once you learn a few basic things about variables and how they interact with the numbers you have been using in your math classes for so many years.

Things You'll Need

• Paper
• Pencil

Instructions

How to Simplify Variable Expressions

1. Start by identifying the terms. In a variable expression, a term is a number and variable that are separated from other numbers and variables by a + or - sign. In 3x^2 + 8x + 2y - 7x^2 + 5y - 9x, the terms are 3x^2, 8x, 2y, -7x^2, 5y, and -9x. Notice that the - sign stays with the term.

2. Identify any like terms. Like terms are terms that have the same variable with either the same power or exponent. In the example you have three pairs of like terms. These are 3x^2 and -7x^2, 8x and -9x, and 2y and 5y.

3. Combine like terms. To do this, add the coefficient, or the number in front of the variable, and carry over the variable and the exponent. This will give you -4x^2 - 1x + 7y.

4. Distribute any terms that need to be multiplied to the entire equation. For instance, in 3x (5x +2y) has a term, 3x, that needs to be distributed and multiplied to both the 5x and the 2y. This gives you 15x^2 + 6xy, which cannot be simplified further because there are no like terms.

5. Use the FOIL method when simplifying variable expressions that include two binomials that are being multiplied together, such as (3x + 4y) (2x - 7y). FOIL stands for First, Outer, Inner, Last, and this represents the order that you will multiply the terms.

6. Multiply the first terms in each binomial, which are 3x and 2x in this example. This gives you 6x^2. Then multiply the outer terms, which are 3x and -7y. This gives you -21xy.

7. Continue by multiplying the inner terms, 4y and 2x, to get 8xy. Finish by multiplying the last terms, which are 4y and -7y, giving you -28y^2. Combine these into one expression: 6x^2 -21xy + 8xy - 28y^2. Combine like terms to get 6x^2 - 13 xy - 28y^2.

Tips & Warnings

• Remember that like terms can be confusing if the order of the variables is switched. For instance, 3xy and 4yx are like terms, even though the x and y are switched. To avoid this problem, always write variables in alphabetical order.

• Always check for like terms when you think you are done simplifying an expression.

Resources

• Read this Article in Spanish
• What Is Simplifying?
• Simplifying Variable Expressions Worksheets