Learn combining like terms
Like terms have identical variable parts. Combine their coefficients, then combine constants separately to simplify an expression.
You will identify like terms and combine only the parts that truly match.
The idea in plain English
Like terms are the same kind of item. Three apples plus two apples makes five apples; 3x + 2x makes 5x.
A plain number is not the same kind of term as an x-term, so they stay separate.
How to recognise this kind of question
- There is no equals sign to solve.
- Several terms repeat the same variable and exponent.
- The instruction says simplify or combine like terms.
Quick decision: Match the variable part exactly, then add or subtract only the coefficients.
The method
- Identify terms with the same variable and exponent.
- Add or subtract the coefficients of matching terms.
- Combine constants and write the simplified expression.
Worked examples
3x + 5 + 2x − 7
- Combine 3x + 2x to get 5x.
- Combine 5 − 7 to get −2.
Answer: 5x − 2
7a − 3 + 2a + 8
- Group 7a + 2a and −3 + 8.
- Add coefficients: 9a. Add constants: 5.
Answer: 9a + 5
Your turn—with help
4x + 9 − x − 2
Need a hint?
Group x-terms and plain numbers separately.
Show the answer and steps
- 4x − x = 3x.
- 9 − 2 = 7.
- Write the two parts together: 3x + 7.
Answer: 3x + 7
Watch out for this mistake
Incorrect: 3x + 5 = 8x
Why it fails: An x-term and a plain number are different kinds of terms.
Do this instead: Leave the expression as 3x + 5.
Quick check
Try these without looking. Then open each answer to check your thinking.
2y + 5y
Need a hint?
Both terms are y-terms.
Show the answer and steps
- Add the coefficients: 2 + 5 = 7.
Answer: 7y
6m + 4 − 2m
Need a hint?
Keep the constant separate.
Show the answer and steps
- 6m − 2m = 4m.
- The +4 stays.
Answer: 4m + 4
3a + 2b + a
Need a hint?
Only the a-terms match.
Show the answer and steps
- 3a + a = 4a.
- The 2b cannot combine with a-terms.
Answer: 4a + 2b
Common mistakes
- Combining a variable term with a constant.
- Changing the variable or its exponent.
- Ignoring the sign immediately before a term.
Practice tips
- Underline variable terms and circle constants.
- Rewrite subtraction as adding a negative when signs feel unclear.