Terms – The Parts of an Expression
A term is a single part of an algebraic expression. Understanding terms is the key to reading and rearranging expressions correctly.
The word “monomial” (a single term) comes from the Greek monos (“one”) combined with the Latin-derived “-nomial” from nomen (“name” or “term”), the same root shared by “binomial” (two terms) and “polynomial” (many terms). The idea of a term’s “degree” matters well beyond naming — it determines how an expression behaves: a degree-1 (linear) term changes at a constant rate, while a degree-2 (quadratic) term changes at an accelerating rate, which is exactly why a linear equation graphs as a straight line and a quadratic graphs as a curve.
What Is a Term?
A term is a product of numbers and/or variables. Terms are separated from each other by addition or subtraction signs. A single term is called a monomial.
Types of Terms
| Type | Example | Description |
|---|---|---|
| Constant term | 7 | A number with no variable |
| Linear term | 5x | Variable to the power of 1 |
| Quadratic term | 3x squared | Variable to the power of 2 |
| Cubic term | 2x cubed | Variable to the power of 3 |
| Mixed term | 4xy | Product of two variables |
Identifying Terms in an Expression
Term 1: 4x squared. Term 2: -3x (the minus sign belongs to this term). Term 3: 8. Answer: 3 terms.
2a, 5b, -ab, -1. Answer: 4 terms.
Coefficients of Terms
The coefficient is the numerical part of a term. It shows how many of that term there are.
| Term | Coefficient | Variable Part |
|---|---|---|
| 7x | 7 | x |
| -3y squared | -3 | y squared |
| x | 1 (invisible) | x |
| -ab | -1 (invisible) | ab |
Degree of a Term
The degree is the sum of all the exponents on the variables in a term.
| Term | Degree |
|---|---|
| 8 | 0 |
| 5x | 1 |
| 3x squared | 2 |
| 2x squared y | 3 (2+1) |
Key Takeaways
- Terms are the building blocks of expressions, separated by + or - signs.
- Each term has a coefficient (which can be 1 or -1 without being written) and a variable part.
- The degree of a term is the sum of the powers of all its variables.