# Algebraic Expression: Definition, Types, Applications, and Examples

Publish Date: 08 Aug, 2023

The history of algebraic expression started with the history of Algebra and the Muslim mathematician Muhammad ibn Musa al-Khwarizmi is known as the “father of algebra”. The history of an algebraic expression is the same as that of the algebraic equation.

## What is Algebraic Expression?

An algebraic expression is a mathematical phrase that uses variables, constants, and mathematical operations like subtraction, addition, multiplication, and division. The exact value is calculated by substituting the value of the variable and applying the mathematical operations to it.

In other words, we can say that an algebraic expression is a statement or expression in which variables, constants, and arithmetic operations are used.

## Representation of Algebraic Expression

Here is the general representation of algebraic expression.

`ax + b`

Here,

• a is a coefficient of “x” always having an integer value
• x is a variable used in this expression
• b is a constant
• + is a mathematical operation

## Types of Algebraic Expression

The algebraic expression has several types but the main type which is most commonly used are as follows:

• Monomial
• Binomial
• Polynomial
• Numeric
• Variable

### Monomial expression

A type of algebraic expression in which there exists only one term is known as a monomial expression. For example,

`3x, 2xy, sqrt (3).`

These are the terms that are known as monomial expressions because there is no plus, minus, multiply, or divide mathematical operation used in them. Just, a single term is used so that we can say that this is a monomial expression.

### Binomial expression

It is a type of algebraic expression in which two terms are used with any mathematical operation known as binomial expression.

For example,

`5x + 8, 36 + 3y, sqrt (x) + 1.`

These are the expressions that are known as binomial expressions because you can clearly see that two unlike terms are used together with the ‘+’ operation.

### Polynomial expression

The type of algebraic expression in which more the one or two terms are used with a non-zero exponent is known as a polynomial expression.

For example,

`ax + by + cz.`

This is the expression in which we can see that there are more than one terms used with mathematical operation and also don’t have any zero exponent which shows that this is a polynomial expression.

### Numeric expression

A type of algebraic expression in which numbers are used as a term with mathematical operations is known as a numeric expression.

E.g.

`2 + 3, 8 – 10, 1 + 10`.

This is the expression in which numeric terms are used with different mathematical operations. These types of terms are known as numeric expressions.

### Variable expression

A type of algebraic expression in which variables are used as terms with mathematical operations is known as variable expression.

For example,

`x + y, x + 2y, 3x -y`

In the above examples, the terms of the variable are used with different mathematical operations.

## Methodology of Solving Algebraic Expression

The goal of solving an algebraic expression is to find the value of a given variable. We can only solve the expression in one condition which is fulfilled when the expression is equated to something or some value.

An algebraic expression is a combination of variables and constants with different mathematical operations such as addition, multiplication, subtraction, and division. When we use these terms together we generate an expression that is known as an algebraic expression.

When we equate it to some value then it becomes an equation that we can easily solve. An algebraic expression is interchangeable means we can keep constant at one place on L.H.S or R.H.S of the equation and variables at one side. In this way, we can easily find the value of a given variable.

## Applications of Algebraic Expressions in daily life

Here are some uses of algebraic expressions are as follows:

• ### Science

Algebraic expressions are widely used in different branches of science such as chemistry, physics, math, and computer science. For example, in physics, we used the expression “W= f*d”. This algebraic expression is used for finding the work done.

• ### Engineering

Algebraic expressions are also used in engineering fields. Engineers have used this expression for describing the behavior of machines or other than this.

• ### Economics

Economists also used algebraic expressions for better acknowledgment of the economic ups and downs of a country or world. These expressions help a lot to sort out the issues related to the economy.

• ### Computer Science

Algebraic expressions are used in programming on a large scale. These expressions are also developed as an algorithm for the ease of programming. Programming is impossible without these expressions.

• ### Statistics

Algebraic expressions are also used in statistics for finding the population or these types of variables. Statistics is incomplete without these expressions. An algebraic expression plays a vital role in the deep understanding of statistics.

## How to Write a Simple Form of Algebraic Expression?

Example

Write the simple form of algebraic expression given below:

2 (3x + 2y) + 2 (4y – 3x)

Solution:

Step 1: By using the definition of multiplication

`= 6x + 4y + 8y – 6x`

Step 2: By using the definition of addition and subtraction

= 6x – 6x + 4y + 8y

`= 0x + 12y`

Step 3: Simple form

`= 12y`