---
title: "What Are Like Terms?"
url: https://www.learningloftinstitute.com/glossary/like-terms
source: Learning Loft Institute
language: en
updated: 2026-08-21
section: "Glossary › What Are Like Terms?"
---
# What Are Like Terms?
> **Answer.** Like terms have exactly the same letters raised to exactly the same powers, so they can be added or subtracted into a single term. 3x and 7x are like terms; 3x, 3x², 3xy and 3 are four different kinds and none of them combine. Only the number in front changes.
## Key facts
| | |
| --- | --- |
| Definition | Like terms are terms whose letter parts are identical, including the powers, so they can be added or subtracted into one term. |
| Where students meet it | Grade 6 or 7 mathematics in the first lessons on simplifying expressions, and assumed in every algebraic manipulation from then on. |
| Also known as | Collecting like terms, Similar terms |
## Four terms that look related and are not
3x, 3x², 3xy and 3 all begin with a 3, and none of them can be added to any of the others. What has to match is the letter part in full: which letters appear, and to what power.
x on its own means x¹, so x and x² are as different from each other as x and y are. A term with no letters, like 3, is a constant and is only ever like another constant. Order inside a term does not matter, though — xy and yx are the same thing, so 2xy and 5yx are like terms and add to 7xy.
- 3x — one x, to the power 1
- 3x² — one x, to the power 2: a different kind of term
- 3xy — two different letters multiplied
- 3 — a constant, like only with other constants
## What changes when you collect them
Only the coefficients. In 4a + 3b − a + 2b, the a terms combine to 3a and the b terms to 5b, and at no point does an a become anything other than an a. If the letter part of your answer has changed, something has gone wrong.
The sign in front of a term travels with it. Here −a is really −1a, so 4 − 1 = 3 rather than 4 − 0 = 4, which is the error you get when the invisible 1 is read as nothing at all.
## Multiplying has different rules entirely
Unlike terms cannot be added, but they can always be multiplied. 3a × 5b = 15ab, and 3x × 4x = 12x². The likeness rule governs addition and subtraction only.
This is worth stating plainly because 3x and 4x behave in two ways depending on the operation: added they give 7x, multiplied they give 12x². Both are correct, and a student who has learned 'you can only combine like terms' as a blanket ban will refuse the multiplication.
## Questions
### Are 3x and 3x² like terms?
No. The powers differ, and the power is part of the letter part that has to match. 3x + 3x² stays as it is — there is no simpler way to write it. If you substitute x = 2 you can see why: 6 and 12 are genuinely different quantities that happen to be built from the same letter.
### Why can't 3a + 5b be simplified?
Because a and b are different quantities, and there is no way to say how many of one make the other. The tempting answer 8ab is wrong twice over: it invents a product where an addition was written, and it would give 8 × 2 × 3 = 48 for a = 2 and b = 3 when the true value is 6 + 15 = 21.
### Are xy and yx like terms?
Yes, and they are actually the same term. Multiplication can be done in any order, so xy and yx are identical, which means 2xy + 5yx = 7xy. By convention the letters are written alphabetically, so yx is normally tidied to xy before anything else happens.
### Can you multiply terms that are not alike?
Yes. The rule about like terms restricts adding and subtracting only. 4a × 3b = 12ab and 2x × 5x² = 10x³ are both fine — multiply the coefficients, then multiply the letters, adding the powers of any letter that appears in both.
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