How to Add & Subtract Algebraic Expressions

Adding or subtracting algebraic expressions can be straightforward.

An algebraic expression is an expression that has more than one term. A term in an algebraic expression is an expression "involving letters and/or numbers (called factors), multiplied together," according to Interactive Mathematics. An example of an algebraic expression is 7x + 2y. 7x is one term and 2y is another. 7x has 7 and x as factors. 2y has 2 and y as factors. The number accompanying the letter in each term is known as the coefficient, and the letter itself is known as a variable. When adding and subtracting algebraic expressions, follow these guidelines.

Instructions

1. Find like terms and group these together. Like terms are terms that contain similar variables expressed to the same power.

   3x2 and 5x2 are like terms.

   4x and 5x are like terms.

   -8x2 and 5y2 are not like terms, because the variable is not the same.

2. Add or subtract these like terms, normally. You can only add like to like, or subtract like from like, that is, terms with exactly the same variable and power. For example, in 13x + 7y ' 2x + 6a, grouping like terms yields (13x - 2x) + 7y + 6a.

3. Simplify the equation to solve. Using the example from Step 2, (13x - 2x) + 7y + 6a = 11x + 7y + 6a. You may also present your answer alphabetically as 6a + 11x + 7y, but this is not strictly necessary.

References

• Interactive Mathematics: Addition and Subtraction of Algebraic Expressions