30+ FREE Combining Like Terms Worksheets (Pre Algebra, Linear, 6th Grade, 7th Grade, 8th Grade)

What Are Like Terms?

In algebra, like terms are terms that have the same variable(s) raised to the same exponent. The coefficients (numerical values) of like terms can be added or subtracted, but the variables remain unchanged. This concept is essential for simplifying algebraic expressions and solving equations efficiently.

For example, in the expression 4x + 7x – 3y + 5y – 2, the like terms are:

By combining these like terms, the simplified expression becomes 11x + 2y – 2.

However, terms with different variables or exponents cannot be combined. For example, in 3x² + 4x + 2y, no terms are like terms because they have different variables or exponents.

Why Is Combining Like Terms Important?

Combining like terms is a fundamental skill in algebra that helps simplify equations and expressions. It allows students to:

Mastering this concept builds a strong foundation for advanced math topics such as polynomials, factoring, and equation solving.

How to Identify Like Terms

To effectively combine like terms, follow these steps:

Examples of Like and Unlike Terms

Expression Like Terms Unlike Terms
3x + 5x – 2y + 4y 3x, 5x and -2y, 4y x, y
2a² + 4a + 3a² – 7a 2a², 3a² and 4a, -7a a², a
6m³ – 4m + 2m³ + 5m 6m³, 2m³ and -4m, 5m m³, m

How to Combine Like Terms

To combine like terms in an algebraic expression, follow these simple steps:

For example, simplify the expression:
2x + 3y – 5x + 7y

Step 1: Identify like terms (2x and -5x, 3y and 7y)
Step 2: Combine like terms (2x – 5x = -3x, 3y + 7y = 10y)
Step 3: Final expression: -3x + 10y

Tips for Mastering Combining Like Terms