What is an Algebraic expression?
Fact-checked: March 1, 2026
Definition
A mathematical expression formed by combining constants and variables with arithmetic operations is called an algebraic expression.
Introduction to Algebraic Expressions
In mathematics, numbers, variables, and arithmetic operators are combined to describe quantities in a clear and structured way. These elements represent values and relationships using mathematical symbols. This mathematical form is called an algebraic expression.
An algebraic expression may include different types of arithmetic operations such as addition, subtraction, multiplication, division, and exponents. These operations are used to combine constants and variables in various ways to represent mathematical relationships.
Let’s look at an example to better understand the concept of an algebraic expression.
Example
$2x^2+6x-5$
In this example, $2$, $6$, and $−5$ are numbers, $x$ is a variable, and the symbols $+$ and $−$ are arithmetic operators used to combine these elements into a structured mathematical form called an algebraic expression.
Examples of Algebraic Expressions
Now that you understand what an algebraic expression is, let’s examine a few additional examples to develop a clearer and deeper understanding of the concept.
Examples
The following are three examples of simple algebraic expressions.
- $5a$
- $-2x$
- $x+3$
Examples
Below are three examples of algebraic expressions with multiple terms.
- $2a+3$
- $4x-y$
- $2l+3m-4n$
Examples
The following are three examples of algebraic expressions with exponents.
- $a^2$
- $2x^3+\dfrac{1}{5}$
- $3x^2-4x-y$
Examples
Below are three examples of algebraic expressions with parentheses.
- $2(a+4)$
- $(x+3)(x-3)$
- $6(x^2+1)\Big(\dfrac{2x}{7}-3\Big)$
The above examples clearly illustrate how numbers, variables, and arithmetic operators are combined to form algebraic expressions in mathematics.
What Does an Algebraic Expression Represent?
An algebraic expression represents a value or a mathematical relationship using numbers, variables, and arithmetic operations. The value of the expression depends on the values assigned to its variables. It provides a symbolic way to describe quantities and how they are related in mathematics.
Example
$2x^2-5$
In this example, the value changes depending on the value of $x$. This shows how an algebraic expression represents both a quantity and the relationship between numbers and variables.
