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What Is a Term in Math?
A term is a single piece of an algebraic expression, separated from the others by a plus or minus sign. In 5x + 3 there are two terms: 5x and 3. This guide covers how to count terms, what makes two of them alike enough to combine, the names for expressions with one, two or three terms, and the difference between a term and a factor. The simplify calculator collects like terms for you.
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What is a term in math?
A term is a single piece of an algebraic expression, separated from the others by a plus or minus sign. In 5x + 3 there are two terms: 5x and 3.
A term can be a plain number, a variable on its own, or numbers and variables multiplied together. What it cannot contain is an addition or a subtraction — those are exactly the boundaries between terms.
Term vs coefficient vs constant
The four words that describe the parts of an algebraic expression are best learned together, because each is defined partly by the others. Take 5x + 3:
| Part | In 5x + 3 | What it is |
|---|---|---|
| Term | 5x and 3 | A piece separated by + or − |
| Coefficient | 5 | The number multiplying the variable |
| Variable | x | The letter standing for an unknown |
| Constant | 3 | A fixed number with no variable |
The term is the part this page is about. The companion guides cover what a term is, what a coefficient is, what a variable is and what a constant is — between them they name every piece of 5x + 3 exactly once.
How to count the terms
Split the expression at every plus and minus sign. Each piece is a term, and the sign in front of a piece belongs to it.
- 5x + 3 → two terms: 5x and 3
- 4x² − 2x + 7 → three terms: 4x², −2x and 7
- 3xy → ONE term. Multiplication does not split anything.
That last case is the one worth pausing on. 3xy looks like three things and is one term, because the pieces are multiplied rather than added. Multiplication and division live INSIDE a term; addition and subtraction live BETWEEN terms.
Like terms
Two terms are like when their variable parts are identical, powers included. Only like terms can be combined.
- 3x + 5x = 8x — like, so the coefficients add.
- 3x + 5y — not like. This does not simplify.
- 3x + 5x² — not like either. The powers differ, so they are different kinds of thing.
The coefficients are what actually get added; the variable part comes along unchanged. That is why what a coefficient is and this page are really two views of the same operation.
Monomial, binomial, trinomial
Expressions are named for how many terms they contain.
| Terms | Name | Example |
|---|---|---|
| 1 | Monomial | 5x |
| 2 | Binomial | 5x + 3 |
| 3 | Trinomial | x² + 5x + 6 |
Beyond three there is no special word in common use and the general term polynomial covers them all, including the three above. The polynomial calculator works with any number of terms.
Term vs factor
These two are the pieces of an expression under two different operations, and swapping them is a frequent error.
- Terms are separated by plus and minus. In 5x + 3 the terms are 5x and 3.
- Factors are joined by multiplication. Within the term 5x the factors are 5 and x.
So terms and factors are not competing descriptions; they sit at different levels. An expression has terms, and each term has factors. The factor guide covers the multiplication side in full.
Common mistakes
- Splitting at a multiplication. 3xy is one term.
- Leaving the sign behind. The second term of 4x² − 2x is −2x.
- Combining unlike terms. 3x + 5y does not simplify.
- Confusing terms with factors. Terms add; factors multiply.
Quick summary
- A term is a piece of an expression separated by + or −.
- The sign in front belongs to the term.
- Like terms have identical variable parts, powers included.
- Terms are added; factors are multiplied.