What Are Like Terms?

Algebraic expressions are made up of letters and numbers. We call the letter the unknown. When a letter and number are together, such as 2b, we call this a term. When we simplify algebraic expressions we collect the like terms together.

The example below shows terms which are alike and terms that are not alike. a and 7a are “like terms” for example. However a and a² are not like terms. ab and -2ab are “like terms”. However ab and a²b are not like terms. a and b are not like terms.

Collecting Like Terms Questions and Answers 1

The example below shows a + 7a - 3a. The answer is 5a. The second part shows  9b + a - 5a. The answer is 4b + a.

Collecting Like Terms Questions and Answers 2

The example below shows 12x + 8y + 3x + 6y. The like terms have been shaded with the same colour. The y terms are green and the x terms are shaded purple. The answer is 15x + 14y.

The second section shows 7t + 10s - 5t - 2s. The answer is 2t + 8s.

How to Collect Like Terms

Algebraic pyramid type exercises work well when learning how to simplify expressions. How the pyramids work is by adding the two blocks, or bricks, which are below. Teachers may even want to make up their own pyramids from a sheet of blank prymaids. You can omit or delete any block to make the problem more difficult, or you can include fractions, decimals and negatives alongside the algebraic expression for more advanced students. Here are some blank pyramids to help along the way...

Collecting Like Terms Questions and Answers 3

The collecting like terms examples below are trickier. The answers are 5k - 6p and - 7q + ab - a.