30+ Combining Like Terms Worksheet Samples to Download

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:

• 4x and 7x (same variable “x”)
• -3y and 5y (same variable “y”)

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:

• Simplifies expressions – Reduces the complexity of algebraic equations, making them easier to work with.
• Prepares for solving equations – Helps in isolating variables to solve for unknown values.
• Strengthens algebraic foundations – Essential for understanding polynomials, factoring, and algebraic operations.
• Improves problem-solving efficiency – Speeds up calculations and logical thinking in algebra.
• Applies to real-world problems – Helps in understanding financial calculations, measurements, and scientific formulas.

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:

• Look at the variables and exponents – Like terms must have the exact same variable(s) and exponent(s).
• Check the coefficients – The numerical value in front of a variable can change, but the variable itself must be the same.
• Ignore constant terms – Numbers without variables (like -5 or 10) are separate and cannot be combined with variable terms.

Examples of Like and Unlike Terms

How to Combine Like Terms

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

• Identify like terms – Look for terms that have the same variable(s) and exponent(s).
• Group the like terms – Rearrange the expression if necessary to place like terms together.
• Add or subtract the coefficients – Keep the variable unchanged while performing the arithmetic operation.
• Rewrite the simplified expression – Ensure that no further like terms exist.

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

• Use color coding – Highlight like terms in different colors to visualize the grouping.
• Rewrite expressions neatly – Organize terms properly to avoid mistakes.
• Double-check signs – Pay attention to positive and negative coefficients.
• Practice with real-world examples – Apply like terms in shopping receipts, budgeting, and physics formulas.
• Work with peers – Solving problems with classmates helps reinforce understanding.