How can I simplify an expression with like terms?
Quick answer
Group terms that have exactly the same variables raised to the same powers; constants match other constants. Add or subtract the number coefficients within each group, keeping the shared variable part unchanged. For example, 5x + 3 − 2x + 7 becomes 3x + 10. Do not combine x with x²: the letter matches, but the powers do not. [S1]
The question, the details, the next step.
How do I tell which terms are like terms before I start simplifying?
Look at the variable part of each term—the letters and their powers—and set aside the number in front as its coefficient. Terms are like terms only when those variable parts match exactly; constants match constants. Then you can sort terms into groups before doing any arithmetic. [S1]
For example, in 6y, −2y, 4, and 9, the groups are (6y, −2y) and (4, 9). The first pair has the same variable part, y; the second pair consists of constants. This sorting step helps prevent you from combining terms just because their coefficients look convenient.
Can you work through an expression that has both variables and constants?
Try 5x + 3 − 2x + 7. First sort by matching variable parts: the x-terms are 5x and −2x; the constants are 3 and 7. Combine within each group: 5x − 2x = 3x, and 3 + 7 = 10. So the simplified expression is 3x + 10. [S1]
Notice that the minus sign belongs to the term after it: the coefficient of −2x is −2, not positive 2. As a quick check, compare the grouped amounts: both expressions contain 3x and 10. Keep the two groups separate; x and a plain number are not like terms.
What about terms with the same letter but different powers, like x and x²?
They are not like terms. The variable parts have to match in both letters and powers, so x and x² stay in separate groups. Using x and x² in one expression does not make their powers interchangeable. [S1]
For instance, simplify 4a + 2a² − a + 5a². Sort it as (2a², 5a²) and (4a, −a). Combine each group: 2a² + 5a² = 7a², while 4a − a = 3a. The result is 7a² + 3a. You cannot combine those two final terms with each other, because one has a² and the other has a.
How can I check my own answer and avoid a common mistake?
Use a two-pass check. First, scan the original expression and make sure every term went into a group with an identical variable part. Second, check the arithmetic inside each group, including signs, and make sure you kept the shared variable part unchanged. [S1]
Practice: simplify 3m + 8 − m + 2. The m-terms give 3m − m = 2m; the constants give 8 + 2 = 10. The answer is 2m + 10. A tempting mistake would be to combine 2m and 10 into 12m or 12; they are different kinds of terms and must remain separate. If your answer has one term for each matching group, review the signs and coefficients once more.
A practical checklist
List each term separately, keeping its sign attached.
Group terms only when their variables and powers match exactly.
Put constants in a group separate from variable terms.
Add or subtract the coefficients within each group; keep the shared variable part.
Check signs and confirm unlike groups remain separate.
A few more useful answers
Can I combine 3x and 3x² because they have the same coefficient?
No. Their variable parts differ because the powers differ, so they are not like terms. Matching coefficients alone is not enough. [S1]
Can I combine a constant such as 6 with 2y?
No. A constant and a term with a variable belong to different groups. Keep them separate in the simplified expression. [S1]
Sources
References used for this guide.
- [S1] OpenStax Elementary Algebra 2e: Use the Language of Algebra openstax.org · Checked