3x and 8x
Both terms have the variable part x, so their coefficients can be combined.
Free Pre-Algebra Guide
Combining Like Terms
Learn how to identify like terms, combine their coefficients, keep unlike terms separate, and simplify expressions with positive and negative values.
Combining like terms is one of the most important skills in early algebra. Terms can be combined only when they have the same variable part. Once the like terms are identified, add or subtract their coefficients while keeping the variable part unchanged. Constants combine with other constants.
On This Page
- What terms, coefficients, and constants are
- What makes terms like terms
- Why unlike terms cannot be combined
- How to combine coefficients
- How to combine constants
- Working with negative terms
- Expressions with multiple variables
- Groups of three or more like terms
- Worked examples
- Common mistakes
- A reliable strategy
- Interactive practice
Terms, Coefficients, Variables, and Constants
An algebraic expression is made of terms separated by addition or subtraction. A term may contain a number, a variable, or both.
3x + 7 + 5x − 2
3x and 5x are variable terms.
Both contain the variable x.
Both contain the variable x.
3 and 5 are coefficients.
A coefficient is the number multiplying a variable.
A coefficient is the number multiplying a variable.
7 and −2 are constants.
Constants are number-only terms.
Constants are number-only terms.
What Are Like Terms?
Like terms have exactly the same variable part. The coefficients do not need to match. For example, 3x and 8x are like terms because both have x. Likewise, −4y and 9y are like terms.
−4y and 11y
The signs and coefficients are different, but the variable part y matches.
Constants Are Like Terms Too
All constants are like terms with one another. In 4x + 7 − 3, the terms 7 and −3 can be combined because neither contains a variable.
Why Unlike Terms Cannot Be Combined
Terms with different variable parts represent different quantities. You cannot combine x-terms with y-terms, and you cannot combine a variable term with a constant.
| Terms | Like? | Reason |
|---|---|---|
| 3x and 9x | Yes | Same variable part: x |
| 4y and −2y | Yes | Same variable part: y |
| 5 and −8 | Yes | Both are constants |
| 3x and 3y | No | Different variables |
| 7x and 7 | No | One has x; one is a constant |
How to Combine Coefficients
Once you know the terms are alike, add or subtract their coefficients. The variable part stays exactly the same.
Example: 3x + 5x
3x + 5x = (3 + 5)x
3x + 5x = 8x
Write the Variable in the Answer
If 6x + 2x = 8x, the answer is not just 8. The x must remain because you combined the coefficients, not the variable itself.
Combining Constants
Constants are terms without variables. They combine with other constants using ordinary addition and subtraction.
Example: 4x + 7 + 2x − 3
Group like terms
4x + 2x + 7 − 3
Combine x-terms
6x + 7 − 3
Combine constants
6x + 4
Combining Like Terms With Negative Numbers
A subtraction sign can be treated as part of the term that follows it. That makes it easier to combine signed coefficients correctly.
6x − 9x
6x + (−9x) = −3x
−4m − 7m
−4m + (−7m) = −11m
Expressions With Multiple Variables
If an expression contains more than one variable, create a separate group for each variable. Combine all x-terms together, all y-terms together, and so on.
Example: 3m − 10z + 2m − 6z
m-group
3m + 2m = 5m
z-group
−10z − 6z = −16z
Simplified expression
5m − 16z
Three or More Like Terms
A like-term group can contain more than two terms. If three x-terms appear, combine all three coefficients together. The same rule applies to three or more constants.
Example: 2x + 7x − 4x
(2 + 7 − 4)x = 5x
2x + 7x − 4x = 5x
Example: −10 − 5 − 7
−10 + (−5) + (−7) = −22
All three constants belong to one like-term group.
Worked Combining Like Terms Examples
3x + 8x
- The variable parts match.
- Add the coefficients: 3 + 8 = 11.
- Result: 11x.
5x + 7 + 2x − 4
- Combine 5x and 2x to get 7x.
- Combine 7 and −4 to get 3.
- Result: 7x + 3.
4y − 9y + 2
- Use coefficients 4 and −9.
- 4 + (−9) = −5.
- Result: −5y + 2.
3x + 4y + 5x − y
- x-terms: 3x + 5x = 8x.
- y-terms: 4y − y = 3y.
- Result: 8x + 3y.
2m − 6m + 9m
- Add the coefficients: 2 − 6 + 9.
- The coefficient is 5.
- Result: 5m.
−4y − 10 + 3y − 5 − 7
- y-terms: −4y + 3y = −y.
- Constants: −10 − 5 − 7 = −22.
- Result: −y − 22.
Common Mistakes When Combining Like Terms
Combining Unlike Variables
3x + 4y cannot become 7xy or 7x. The terms have different variable parts.
Dropping the Variable
5x + 2x = 7x, not 7. The x remains attached to the combined coefficient.
Ignoring a Negative Sign
In 6x − 9x, the second coefficient is −9, so the result is −3x.
Combining a Constant With a Variable Term
4x + 7 cannot be simplified to 11x. The constant 7 is not an x-term.
Treating Three Like Terms as Separate Pairs
If 2x, 5x, and −3x all appear, they form one group. Combine all three coefficients.
Changing the Variable Part
Adding coefficients does not add variables. 3x + 2x = 5x, not 5x².
A Reliable Strategy for Combining Like Terms
1. Identify every term
Include the sign directly in front of each term.
2. Group like terms
Put terms with identical variable parts together; group constants together.
3. Combine coefficients
Add or subtract the coefficients in each variable group.
4. Keep the variable part
Write the correct variable with every combined coefficient.
5. Combine constants
Add or subtract all number-only terms.
6. Write the simplified expression
Keep unlike variable groups separate.
Quick test: same variable part = combine; different variable part = keep separate.
Practice Combining Like Terms
Identify all like-term groups, combine complete variable terms, simplify constants, and build the expression one step at a time.
Open the Combining Like Terms ToolRelated Math Resources
Personalized Math Support
Need Help Making Sense of the Math?
If a concept still feels confusing, you do not have to work through it alone. Tell me what you are studying and where you are getting stuck, and I will help you determine the best next step.