Collecting Like Terms: Definition, Examples, and Questions

Collecting like terms is an important step in simplifying algebraic expressions. In this lesson, you'll learn what like terms are, how to collect like terms, and you'll see some examples to help you practice.

What are Like Terms?

Like terms are terms that have the same variable or combination of variables raised to the same power. Only like terms can be added or subtracted in algebraic expressions.

For example:

How to Collect Like Terms

  1. Identify the like terms in the expression.
  2. Group the like terms together (including their signs).
  3. Add or subtract the coefficients of the like terms.

Examples of Collecting Like Terms

Example 1:

Simplify 3c + 8c - 2c

Solution:

Answer: 9c

Example 2:

Simplify 5f + 8 + 13f + 3

Solution:

Answer: 18f + 11

Example 3:

Simplify 3a + 2b + 13 + 7a + 3b + 4

Solution:

Answer: 10a + 5b + 17

Collecting Like Terms Practice Questions

Question 1

Simplify: \( 3a + 5a - 2a \)

Collecting Like Terms with Powers

Example 4:

Simplify 2x + 3x² + 5x

Solution:

Answer: 7x + 3x²

Example 5:

Simplify x² - 5x + 4x² - 4 + 7x

Solution:

Answer: 5x² + 2x - 4

Example 6:

Simplify ab² - 3a²b + 4ab² - 4a²b² + 7a²b

Solution:

Answer: 5ab² + 4a²b - 4a²b²

Collecting Like Terms Practice Questions (Including Powers)

Question 1

Simplify: \( 4x^2 + 3x - x^2 + 2x \)