If you’re studying algebra, you’ve likely come across the term “term” before. In algebra, a term refers to a single number, variable, or a combination of numbers and variables that are separated by mathematical operators. Understanding what a term is and how to work with them is essential to solving algebraic equations and expressions.
Terms are the building blocks of algebraic expressions, which are mathematical sentences that contain variables, numbers, and mathematical operators. A term can be a single number, variable, or a combination of both that are multiplied together. For example, in the expression $5x + 3y$, $5x$ and $3y$ are both terms. In this case, $5$ and $3$ are coefficients, which are numbers that are multiplied by the variables.
It’s important to note that terms are separated by addition or subtraction signs in algebraic expressions. For instance, in the expression $2x + 3y - 7$, there are three terms: $2x$, $3y$, and $-7$.
What is a Term in Algebra?
In algebra, a term is a single number, variable, or a combination of both. Each term is separated by a mathematical operator.
Example: in $3x + 2y - 5$, the terms are $3x$, $2y$, and $-5$.
A term can also be a constant, which is a number without a variable. For example, in $4x + 7$, the term $7$ is a constant.
Types of Terms
| Type of Term | Definition |
|---|---|
| Monomial | A term with only one variable. |
| Binomial | Two terms separated by an operator. |
| Trinomial | Three terms separated by operators. |
Example: $2x^2 + 3xy - 4y^2$ has:
- Monomial: $2x^2$
- Binomial: $3xy$
- Monomial: $-4y^2$
(Note: Some descriptions may mix “terms” and “expressions” — a binomial and trinomial are expressions, not terms.)
Operations With Like Terms
Like terms have the same variables with the same exponents.
Addition/Subtraction
Example:
$3x + 2y - 5x + 4 \Rightarrow (3x - 5x) + 2y + 4 = -2x + 2y + 4$
Non-like terms can’t be combined, e.g., $3x + 3x^2 \ne 6x^2$
But: $3x^2 + 3x^2 = 6x^2$
Multiplication
Multiply coefficients and add exponents:
$2x^2 \times 3x^3 = 6x^{2 + 3} = 6x^5$
Division
Divide coefficients and subtract exponents:
$6x^5 \div 2x^2 = 3x^{5 - 2} = 3x^3$
Examples of Terms in Algebra
- $5$
- $x$
- $2y$
- $3xy$
- $4x^2$
- $5y^2z$
- $-2a$
- $-3b^2$
In $3xy$, the coefficient is $3$; in $-2a$, it’s $-2$.
Example: $4x^2 + 3xy$ is an expression of two terms.
Like Terms
$4x^2$ and $2x^2$ are like terms: $4x^2 + 2x^2 = 6x^2$
Applications of Terms in Algebra
Terms are found in:
- Polynomials: $2x^2 + 3x - 1$ (three terms)
- Equations: $2x + 3 = 7$
- Functions: $f(x) = 2x + 3$
They’re useful in simplifying expressions, solving equations, and forming formulas.
Conclusion
A term is a single number, variable, or combination of both. Terms are separated by $+$ or $-$ in expressions. You can:
- Combine like terms to simplify
- Multiply/divide terms using exponent rules
- Distinguish between terms and factors: $3$ is a factor in $3x$
For example, in $2x + 3$, the coefficient of $x$ is $2$.
Mastering terms helps you simplify, solve, and understand algebra more deeply.