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Combine Like Terms Calculator
Your expression
Use single letters for variables (x, y, z, a, b …). Coefficients can be whole numbers or decimals, and terms can be positive or negative. A lone x means 1x.
2y stays as 2y
5 stays as 5
Example: 3x + 2y − x + 5 simplifies to 2x + 2y + 5.
Behind the numbers
How combining like terms works
Like terms have exactly the same variable part. To combine them, add or subtract their coefficients and keep the variable part unchanged. A term with no number in front of its variable has a coefficient of 1, so x means 1x and −x means −1x. Constants — plain numbers with no variable — combine only with other constants.
Worked example: 3x − x = (3 − 1)x = 2x. The same rule gives 4a − 2a = 2a, and 3b − b = 2b, because b on its own means 1b.
A few comparisons
Example expressions, simplified
| Expression | Simplified |
|---|---|
| 3x + 2y − x + 5 | 2x + 2y + 5 |
| 4a + 3b − 2a + 7 − b | 2a + 2b + 7 |
| 2x + 3x | 5x |
| 5 + 3 | 8 |
| 2.5x + 1.5x | 4x |
| 7y − 2y + 4 | 5y + 4 |
Combine without the mistakes.
Underline the variable part of each term first — only terms with the same letters can be combined, so x terms never mix with y terms.
Watch the minus signs: in 3x − x, the second term is −1x, not +1x. A minus in front of a term belongs to that term.
Remember the hidden 1: a lone x is 1x and a lone −x is −1x, so 2x + x is 3x, not 2x.
Constants are their own group. In 3x + 5, the 5 cannot join the 3x — the expression is already as simple as it gets.
Good to know
Your like-terms questions, answered.
What are like terms?
Like terms have exactly the same variable part. 3x and 5x are like terms because both are x terms, and 2y and 7y are like terms. 3x and 3y are not like terms, because x and y are different variables, and 4 and 9 are like terms because both are plain numbers, called constants.
How do you combine like terms?
Group the like terms together, then add or subtract their coefficients and keep the variable part unchanged. For example, 3x + 2y − x + 5 becomes 2x + 2y + 5: the x terms combine as 3x − x = 2x, the 2y stays as it is, and the constant 5 stays as it is.
What does “x” on its own mean?
A lone x means 1x, so its coefficient is 1. Likewise, −x means −1x. That is why 3x − x = 2x: it is 3x − 1x, and 3 − 1 = 2. The same rule applies to any variable, such as y meaning 1y.
Can I combine 3x and 3y?
No. 3x and 3y have different variable parts, so they cannot be added into a single term. The expression 3x + 3y is already simplified. Only terms with the same variable part combine, and constants combine only with other constants.