# What are Algebraic Expressions?

Table of Contents

## What is Algebra?

Algebra is known to be one of the oldest fields in Mathematics that was studied. It is defined as the study of mathematical symbols and includes rules that are used for the manipulation of these symbols. Algebra is the key that unifies mathematical topics. It is very useful for starting a mathematical equation and deriving a relationship making use of letters and symbols that represent the different entities. It can be classified into two broad categories elementary algebra and abstract algebra. Any subject such as science, engineering, medicine, etc. that requires the use of solving equations uses elementary algebra. It also includes deriving the value of unknown quantities.

## Algebraic Expressions

An algebraic expression is a mathematical expression that is made up of constants and variables connected together by algebraic operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic equations should not be confused with algebraic expressions. An algebraic equation should not be confused with an algebraic expression. A mathematical statement in which two expressions are set equal to one another is known as an equation. Equations mean equality; hence, it implies that you are equating one quantity to another.

Example of algebraic expressions

3ab + 5b^{2} – 8

Here, a and b are the variables whose values are unknown to us, 3 and 5 are the coefficients attached to the variables and are well defined, -8 is the constant term. The algebraic operations used are addition, multiplication, subtraction, and exponentiation

Example of algebraic equations:

9x + 3 = 5x – 1

The left-hand side (LHS) is given by 9x + 3, and the right-hand side is given by 5x – 1. These two are algebraic expressions. As they are connected together by an equal sign, it forms an algebraic equation. By solving this equation, we can get the value of the variable x.

9x – 5x = -1 – 3

x = -2

## Types of Algebraic Expressions

### Monomial Expression

An algebraic expression that has only one term is called a monomial expression. For example, 56ab, 3a3, 7 etc.

### Binomial Expression

If an algebraic expression consists of only two variables, it is called a binomial expression. We can consider binomial expressions to be a combination of two monomial expressions that are joined together by an addition or subtraction operator. Examples of binomial expressions are 3yb + xy^{8}, 7y – 9, etc.

### Polynomial Expression

An algebraic expression that has more than one term that does not equal zero and has only non-negative integral exponents of a variable are known as polynomials or polynomial expressions. Examples are an + bm + 5, x^{3} + 98zy – 1 etc.

### Numeric Expression

An algebraic expression that consists of only numbers and operations but does not include variables is known as a numeric equation. For example, 56 + 3, 74 / 2 and so on.

### Variable Expression

Expressions that consist of variables, numbers, and operations are known as variable expressions. Examples of variable expressions are 7y – 8, 36xz + 9 etc.

## Conclusion

Algebra is used in all walks of life directly or indirectly. Thus, it is arguably one of the most important topics that a child will learn during his school career. To ensure that a student gets the best quality of education, he should turn to a coaching institute such as Cuemath. At Cuemath, the certified tutors combine fun with learning to provide kids with an enjoyable learning experience and allow them to maintain flexibility while studying. They use resources such as worksheets, workbooks, math puzzles, and games to deliver a lecture. Hopefully, this article gives you an idea of the importance of algebra, and I wish you all the best!