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What Is an Algebraic Expression and Why Is It Important?

What is an algebraic expression: teenager taking down notes during an online class

What is an algebraic expression? An algebraic expression is a mathematical phrase that uses coefficients, unknown variables, algebraic operations, and constants. However, an expression cannot have an equals sign.

Let's expand on the definition of an algebraic expression and explain how it’s different from other types of mathematical expressions.

What Is an Algebraic Expression?

Let's explore the terms that make up an algebraic expression using the following example:

algebraic expression example

  • The numerical value of 3 represents a coefficient, which is a number used in unison with a variable.
  • In this expression, x is a variable, which is a letter that represents an unknown quantity.
  • The addition sign in this expression is an algebraic operation. Used interchangeably with the phrase “arithmetic operations,” algebraic operations can also be represented by multiplication, division, or subtraction symbols. They can also include a square root or exponent in combination with one of these symbols.
  • The quantity of 14 represents a constant, which is a number that has a clearly defined value.

All of these terms must be present in order to classify as an algebraic expression.

Expressions and Equations

There are many different types of mathematical expressions and phrases. Let's explore how algebraic equations and numerical expressions relate to algebraic expressions.

Algebraic Equations

The one thing that separates an algebraic expression from an algebraic equation? The latter has an equal sign. Here are some examples of expressions vs. equations:

Algebraic Expressions:

What is an algebraic expression: Algebraic expressions

Algebraic Equations:

Algebraic equations

Numerical Expressions

A numerical expression is a mathematical phrase that only uses algebraic operations and constants. Here are some examples of numeric expressions:

What is an algebraic expression: Numerical expressions

Since numerical expressions don't use variables, they do not classify as algebraic expressions.

Types of Algebraic Expressions

Now that we know what types of mathematical phrases do not classify as algebraic expressions, let's explore the different types of algebraic expressions: binomial expressions, trinomial expressions, and polynomial expressions.

Binomial expressions have two terms (one constant and one variable) and one algebraic operation.

Binomial expression

Trinomial expressions have two algebraic operations and three different terms: one constant and two different variables, one constant and two variables with two different exponents, or three variables with three different exponential values.

What is an algebraic expression: Trinomial expression

Polynomial expressions have four or more terms tied together by multiple algebraic operations:

Polynomial expression

What Is an Algebraic Expression and Why Does It Matter?

When you understand how to identify a coefficient, variable, algebraic operation, and constant, you can start classifying and working with different types of algebraic expressions. You’ll use algebraic expressions throughout many levels of math.

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