How to Use Like Terms to Simplify Algebraic Expressions

Simplifying algebraic expressions becomes very easy once you understand how to use like terms. In this lesson, we will focus on applying like terms correctly to make algebraic expressions shorter, clearer, and easier to solve.

If you are new to algebra, we strongly recommend first reading:

• Polynomial Expressions in Algebra – Definition, Types, and Examples
• Like and Unlike Terms in Algebra – Easy Explanation

What Does It Mean to Simplify an Algebraic Expression?

Simplifying an algebraic expression means combining all like terms to make the expression as short and clear as possible without changing its value.

Example:

3x + 5x = 8x

Here, both terms have the same variable x, so they can be combined.

Rules for Using Like Terms

• Like terms must have the same variable
• The same exponent on the variable
• Only the coefficients are added or subtracted

Step-by-Step Method to Use Like Terms

Step 1: Identify Like Terms

Group terms that have the same variable and exponent.

Step 2: Combine Coefficients

Add or subtract the numbers in front of the variables.

Step 3: Write the Simplified Expression

Keep the variable part unchanged.

Worked Examples

Example 1

2x + 4x − x

= (2 + 4 − 1)x

= 5x

Example 2

3a + 7b − 2a + 5b

= (3a − 2a) + (7b + 5b)

= a + 12b

Example 3 (With Constants)

4x + 6 − 2x + 3

= (4x − 2x) + (6 + 3)

= 2x + 9

Common Mistakes Students Make

• Combining unlike terms (e.g., x + y)
• Forgetting negative signs
• Changing variables while simplifying

Incorrect: 2x + 3y = 5xy 

Correct: 2x + 3y (cannot be simplified)

Why Learning This Skill Is Important

Using like terms correctly helps students:

• Solve equations faster
• Understand polynomials better
• Avoid mistakes in exams
• Prepare for advanced algebra topics

Practice Questions

1. 5x + 3x − 2x
2. 7a + 4b − 3a
3. 6y − 2 + 3y + 5

Solve these.

Related Algebra Lessons

• Polynomial Expressions in Algebra
• Learn Like and Unlike Terms in Algebra

Final Thoughts

Learning how to use like terms is a key step in mastering algebra. With regular practice and careful attention to rules, simplifying expressions becomes quick and enjoyable.

* Keep practicing, and explore more algebra lessons on LuminousNaeem to strengthen your math skills.