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.
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
How many terms does 4x squared - 3x + 8 have?
Term 1: 4x squared. Term 2: -3x (the minus sign belongs to this term). Term 3: 8. Answer: 3 terms.
List the terms of 2a + 5b - ab - 1.
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.
Practice Questions
- List all terms in: 6y cubed - 4y + y squared - 9.
- What is the coefficient of x squared in: 3x + 5x squared - 7?
- What is the degree of the term 4a squared b cubed?
- Write a 3-term expression with degrees 2, 1, and 0.
- In the expression 3p - 2q + pq, which term has two variables?