Expressions in Math

Last Updated : 20 Feb, 2024

In math, an expression is a statement involving at least two different numbers or variables and at least one operation, such as addition, subtraction, multiplication, division, exponents, and roots.

In this article, we will learn about expression, terms, factors and coefficients in expression. We will discuss expression definition, term definition, factor definition, coefficient definition and examples.

Expressions in Maths

Table of Content

What is Expression in Math?
How to Write Expression in Math?
Types of Expression
Examples of Expression
Factors of Expression
Equation vs Expressions in Math

What is Expression in Math?

In mathematics, an expression is a statement consisting of at least two numbers, variables, and at least one operators (such as addition, subtraction, multiplication, or division).

An expression typically involves at least two terms connected by an operator. Unlike equations, expressions do not contain an equality sign (‘=’). Some examples of expression include:

2x + 3y
5a − 2b
3/4 x + 2
7 + 2 × 5

Expression Definition

An expression in mathematics is a finite combination of constant or variable using operators such as addition (+), subtraction (-), multiplication (×), or division (÷).

Some key points regarding expressions are:

Expressions do not contain an equality sign (“=”)
Constants, variables, or products of variables and constants are considered terms
When a variable is multiplied by a constant, the constant is referred to as a coefficient

Terms used to Explain Expression

Some common terms used in the explanation of expression are:

Variable
Constant
Coefficients

Variable

A symbol that has variable values or that can be assigned different numerical values is called a variable in an algebraic expression.

Typically, a letter from the English alphabet is used to represent a variable. For instance, x, y, z, i, c or a, b, c, etc.

Constant

A symbol in an algebraic expression with a fixed numerical value is called a constant.

For instance, 7, -5, and 0, 3/5, etc. are all constants.

Coefficients

In mathematics, a coefficient is a multiplicative factor involving a number or a variable in a term of a polynomial, series, or expression.

Coefficients can be either numeric values (constants) or letters standing for constants. For instance, in the term 7x, the coefficient is 7, and in -9y², the coefficient is -9.

Note: Coefficients can be positive, negative, real, complex, rational, irrational, decimal, or fractional.

How to Write Expression in Math?

To write an expression in math, you need to use a combination of numbers, variables, and operational symbols.

Step 1: Interpret the given text or phrase, identifying key words related to arithmetic operations (e.g., addition, subtraction, multiplication, division)

Step 2: Replace those key words with appropriate mathematical symbols (e.g., +, -, ×, ÷).

and with “+”
from with “-“
of with “×”
by with “÷”
Step 3: Apply the order of operations when necessary, especially when dealing with multiple operations in a single expression.

Step 4: Simply.

For example, to write the expression for “The sum of 7 and the product of -2 and x”: 7 + (−2 × x) = 7 – 2x

Types of Expression

Expressions are mathematical statements that combine variables, constants, and operators. There are different types of expressions, including:

Numerical Expression
Algebraic Expression
Radical Expression
Fractional Expression

Let’s discuss these in detail as follows.

Numerical Expression

A numerical expression is a specific type of mathematical expression that involves numerals (constants) and arithmetic operations.

It produces a result that is either a number or a boolean value when evaluated. Some examples of numerical expressions include:

5 – 2 + 1/2 (a simple constant expression)
5 + 2 – (3 × (-1) + 7) (this can be simplified to 3)
3 × (8 + 4) – 7 (this can be simplified to 29)

Algebraic Expression

An algebraic expression is a mathematical expression that consists of variables, constants, and algebraic operations such as addition, subtraction, multiplication, division, and exponentiation.

Some examples of algebraic expression are:

3x – 3xy³ (monomila expression)
5xy + 8 (binomial expressions)
ax + by + c (polynomial expressions)

Fractional Expression

A fractional expression contains fractions within an algebraic expression. For instance, consider the following examples:

$\frac{3}{x}+\frac{9}{20}$
$\frac{x-2}{x+2} + 2$
$\frac{3}{x-3} - \frac{1}{2}$
$\frac{4x^2}{x-5}$

Radical Expression

A radical expression is a mathematical expression that contains a root symbol, such as a square root, cube root, or fourth root. Examples for radical expression include:

$3\sqrt{2}$ – 7
$\sqrt{9x^2}$ + 1/2
$\sqrt{x^2 + 2x - 1}$

Examples of Expression

There can be various example of expression involving various different function, constant or variable. Some common examples include:

Polynomial Expression
Trigonometric Expression
Logarithmic Expression
Exponantial Expression

Polynomial Expression

All the expression of form with any degree is called polynomial expression. Some examples of polynomial expressions include:

2x² + 3x + 7
a² + 2ab + b²
x⁴ – 2xy² + 3y⁴
x³ – 8x – 11
3x² – 5x³ + 8x + 9x² – 7x + 2x³
2p² – 7
6m³ – mn + n² – 4

Read more about Polynomial.

Trigonometric Expression

Expression containing trigonometric ratios is called onometric Expression. Examples of trigonmetric expression are:

sin²x – 2sin x
sin x + cos x + tan x
sin³x – sin²x + sin x
$\frac{tan \theta}{\cosec \theta} + \frac{sin \theta}{\cot \theta} + \frac{cos \theta}{\cot \theta}$

Read more about Trigonometry.

Logarithmic Expression

A logarithmic expression typically includes a logarithm function, denoted as either log_b (x), where b represents the base of the logarithm. Some examples are:

log₁₀ 100 – log₁₀ 10 + log₁₀ 2
ln x + ln y -ln 2
log_π (π²) – log₁₀ 100

Read more about Logarithm.

Exponantial Expression

Exponential expressions involve exponents and are used to represent repeated multiplication. Some examples of exponantial expression are:

2³ – 3² + 7⁵
10³ -10²

Factors of Expression

A factor of an expression is a number or expression that divides the expression evenly.

For example, in the expression 2x + 4, both 2 and x + 2 are factors of the expression. Some more examples of factors of expression are:

For 3ab + 6c, factors are 3 and ab + 2c.
For x² – 5x + 6, (x – 2) and(x – 3) are the factors.
For 2ab – 6ab², 2b and a + 3ab are the factors.

Read more about Factors.

Equation vs Expressions in Math

The key difference in equation and expression in math is given below:

Feature	Equation	Expression
Structure	Two expressions connected by an “equal to” (=) sign.	Combination of numbers, variables, and operation symbols.
Number of expressions	Two	One
Purpose	Represents an equality between two mathematical statements.	Represents a value or a calculation without requiring equality.
Solution	Often solved to find a specific value for a variable.	Can be simplified to obtain a final value.
Example	2x + 5 = 11	3x² – 2y
Real-world use	Balancing chemical equations, finding distances, calculating speed, etc.	Representing areas, sums, volumes, etc.

Read More About

Solved Examples on Expressions

Example 1: Find the coefficient of term 7y in the expression 6x²+ 7y + 3?

Solution:

The coefficient of term 7y in the expression 6x²+7y +3 is “7”.

Example 2: Find the terms in the expression 5x +6y +3?

Solution:

The no of terms in the expression is 5x , 6y, 3.

Example 3: Find the factors in the expression 7x³+ 5x²+ 6x + 2?

Solution:

The factors in the expression are 7, x³, 5, x², 6, x, 2.

Example 4: What type of algebraic expression is 4x + 5?

Solution:

4x + 5 has two monomials 4x and 5 and hence it is a binomial. Now, since every binomial is a type of polynomial.

Therefore, 4x + 5 is a binomial.

Example 5: Identify the terms and coefficients in the expression 3a²+2ab?

Solution:

There are two terms in the expression 3a², 2ab.

The coefficients in the expression are 3, 2.

Practice Problems on Expressions

Problem 1: Identify the terms in the expression 10x³ + 71x² + 91x − 20x²+ 61.

Problem 2: Identify the terms, factors, coefficients in the expressions given below.

8xy − 13x² + 14x + 5y − 21
x²+ 5x + 7 − 15x

Problem 3: Determine the variable, coefficient, constant, and terms of the algebraic expression 31mn – 16m + 4n + 19.