In Mathematics, Algebra is an interesting topic in which numbers, shapes, and letters form expression. An algebraic expression consists of constant and variables followed by an algebraic operation like addition, subtraction, multiplication, and division.

These Algebraic expressions are made up of terms, and a term is the product of factors. The expression with one term, two terms, or more terms are referred to as ‘monomial, ‘‘Binomial,’ and ‘Polynomial.’
So, the formulas and rules in maths are written in general form using algebraic expression.

For example,
4x-1, 5x+6y+3, etc.

  • Variable is the unknown values represented by letters. For example: In the above expressions x,y are our variables.
  • Constants are definite values. For example: In the above expression, 1 and 3 are the constant numbers.
  • Coefficients is the number placed with or multiplied with a variable in Algebraic expressions. For example, 4,5,6 are the coefficients of x and y.

Moreover, numbers like π and е are not algebraic because they are not derived from any constant or algebraic operations. These expressions are shown with unknown variables, constants, and coefficients and when combined to form an Algebraic expression with no sides or equal to sign.

Algebraic expressions Classification:

There are three types of Algebraic expressions

  • Monomial
    An Algebraic expression with one term is called as Monomial. Example of a monomial: 3x, 7y, etc.
  • Binomial
    An Algebraic expression with two-term is called a Binomial. Example of a monomial: 3x+1, 2xy+7y, etc.
  • Polynomial
    An Algebraic expression with more than one term is called a Polynomial. Example of a monomial: 3x+2y+7, 7x+y, etc.

How to solve the Algebraic Expressions?

In this, we will take a Polynomial expression:

Example 1: Solve the equation?
P(x)=6×2+2x -3 where x=2

Step 1: Put the value of x=2 in the polynomial expression.

P (2) =6(2)2+2(2)-3
Step 2: Use BODMAS rule
P(2)= 6(2*2)+2(2)-3
Step 3: This expression will become
P (2) =6(4) +4-3

As a result, we get the P (2) =25 as the simplified algebraic expression.

Example 2: Determine the value of the variable in the following equation:

Separate the variable and constant terms
Divide both sides by 5
x= 6
As a result, the value of x=6 after simplification.

Algebraic expression formulas

The general formulas used to solve any algebraic expression or equation are:

(a+b) ^2= a^2+b^2+2(ab)
(a-b) ^2= a^2+b^2-2(ab)
a^2-b^2=(a+b) (a-b)
(a+b) ^3= a^3+b^3+3ba(a+b)
(a-b) ^3= a^3-b^3-3ba(a-b)
a^3+b^3=(a+b) (a^2+b^2-ab)
a^3-b^3=(a-b) (a^2+b^2+ab)

Frequently Asked Questions – FAQs

What is a coefficient and variable in an algebraic expression?

The coefficient is the number with the variable, and the variable is the unknown value, which we need to evaluate by solving a given algebraic expression.

Are all the algebraic expressions polynomials?

No, not all the algebraic expressions are algebraic, but all the polynomials are algebraic expressions. Meanwhile, the algebraic expression includes all the relational and irrational numbers, whereas the polynomial is a continuous function.

For example,

Polynomial expression: 6×2+2x -3 (Continuous function)
Algebraic expression: \frac {1} {x+1}

In conclusion, an algebraic expression is a relationship between numbers without specifying what those numbers are. I hope you enjoyed reading the article about-What is Algebraic expression? Did you find this blog post helpful? If so, I’d be very grateful if you’d leave a comment, or sharing it on Twitter or Facebook. Thank you!

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