# What is a Mathematical Expression? - Definition & Examples

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• 0:01 Simplest Math Expressions
• 0:24 Variables in Math Expressions
• 3:13 Identifying Terms &…
• 4:55 Expressions Versus Equations
• 5:20 Lesson Summary
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Lesson Transcript
Instructor: Betty Bundly

Betty has a master's degree in mathematics and 10 years experience teaching college mathematics.

This lesson will explain how to recognize a mathematical expression and the parts that make up a mathematical expression. You will also learn some of the basic vocabulary used when discussing mathematical expressions.

## The Simplest Mathematical Expressions

Our first introduction to mathematical expressions began with arithmetic. A problem as simple as 12 + 2 is a mathematical expression. We could change the (+) to make different mathematical expressions: 12 - 2, 12 * 2, or 12 / 2. Addition, subtraction, multiplication, and division are called operations. There are many more operations that can be used in a mathematical expression.

## Variables in Mathematical Expressions

In algebra, we begin to see variables, or letters that are used to represent numbers. An example of a mathematical expression with a variable is 2x + 3. All variables must have a coefficient, a number that is multiplied by the variable. In the expression 2x + 3, the coefficient of x is the number 2, and it means 2 times x plus 3.

Why isn't the multiplication actually shown? Since x is often used as a variable, in algebra the symbol x is rarely used to show multiplication. Sometimes a dot, an asterisk, or parentheses may be used instead. For example, 2x + 3 could also be expressed as 2(x) + 3 or 2 * x + 3.

What is the coefficient of x in an expression like x + 4? Anytime you don't see the coefficient, a 1 is implied to be there. So, the coefficient of x is understood to be the number 1.

Sometimes, operations are applied directly to a variable in mathematical expressions. For example, in the expression 3x^2, the squaring operation is being applied to the variable x. In the expression 2 * square root y, the square root operation is being applied to the variable y. In these cases, we would say 3x^2 has a coefficient of 3, or 2 * square root y has a coefficient of 2.

Mathematical expressions may be multivariate, which means they have more than one variable. An example of a multivariate expression is 4xy - 5x + 7. Just as 2x means 2 times x, 4xy means 4 times x times y.

Variables may also be in the denominator of a fraction, as in the expression 7x/y.

All mathematical expressions contain parts called terms. The term of a mathematical expression is separated from other terms with either plus or minus signs and consist of the product a coefficient and one or more variables. A single term may contain an expression in parentheses or other grouping symbols. In this case, the grouped expression is part of that term. For example, -2x/(x + 1) is considered 1 term, with a coefficient of -2.

The simplest term, a constant, consists of only a number with no variable. Examples of constants are -2, 0.37, square root of 2, or ¾. What is the coefficient of a constant? A constant is its own coefficient!

## Identifying Terms and Their Coefficients

Now, let's put together everything we learned to identify all the parts of a mathematical expression.

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