Collecting like terms means combining terms that have the same letter part, so an expression becomes shorter without changing its value. The rule is to add or subtract only the numbers in front of identical letters.
What counts as a like term?
Like terms share the same letters raised to the same powers. The table sorts some examples.
| Terms | Like? | Reason |
|---|---|---|
| 4x and 9x | Yes | Both are x |
| 2y and 2x | No | Different letters |
| 5x² and 3x | No | x² and x are different powers |
| 6 and −2 | Yes | Both are plain numbers |
Worked example
Simplify 4x + 5y − x + 2y − 4 + 9. The worked example is built in three layers.
Start with the x terms only. There are +4x and −x, and −x means −1x. So 4x − 1x = 3x.
Next the y terms: +5y and +2y give 7y. Finally the numbers: −4 + 9 = +5.
Put the pieces together: 3x + 7y + 5.
A check by substitution confirms it. Let x = 2 and y = 1. The original gives 8 + 5 − 2 + 2 − 4 + 9 = 18. The answer gives 6 + 7 + 5 = 18.
What does the common mistake look like?
A student simplifies 3a − 5a + 4 as 2a + 4. The error is in the sign: 3a − 5a is −2a, because taking away more than you have gives a negative result. The correct answer is −2a + 4.
The repair is to draw a circle around each term including the sign that comes before it. Then 3a and −5a are the terms, and 3 + (−5) = −2.
Steps to follow
- Circle each term with the sign in front of it.
- Sort the terms by letter part: all x terms, all y terms, all plain numbers.
- Combine each group by adding the coefficients, then write the answer in a sensible order.
Self-check
Simplify 6m − 2n + 3 − 9m + 5n − 8.
Answer
m terms: 6m − 9m = −3m. n terms: −2n + 5n = 3n.
Numbers: 3 − 8 = −5. The answer is −3m + 3n − 5. Check with m = 1 and n = 1: the original is 6 − 2 + 3 − 9 + 5 − 8 = −5, and the answer is −3 + 3 − 5 = −5.
Where to go next
Once simplifying is reliable, move on to expanding and factorising simple expressions. The algebra step repair trainer gives extra practice on the sign step, and the algebra readiness hub shows where this fits. If you want a teacher to watch your working, see Mathematics tuition.