Algebraic Expressions

What is an Algebraic Expression?

Algebraic Expression Definition: An algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations (addition, subtraction, etc.) Expressions are made up of terms.

Example of algebraic expression:

3x+4y -7,  4x – 10 etc.

It is to be noted that, unlike algebraic equation, an algebraic expression has no sides or equal to sign. Some of its examples include

  • 3x+4y -7
  • 4x – 10
  • 2x2−3xy+5

The terminology used in Algebraic expressions:

In Algebra we work with Variable, Symbols or Letters whose value is unknown to us.

In the above expression (i.e. 5x – 3),

  • x is a Variable, whose value is unknown to us which can take any value.
  • 5 is known as the Coefficient of x, as it is a constant value used with the variable term and is well defined.
  • 3 is the Constant value term which has a definite value.

The whole expression is known to be the Binomial term, as it has two unlikely terms.

Types of Algebraic expression:

There are 3 mains types of algebraic expressions which include:

  • Monomial Expression
  • Binomial Expression
  • Polynomial Expression

Monomial Expression

An algebraic expression which is having only one term is known as a monomial.

Examples of monomial expression include 3x4, 3xy, etc.

Binomial Expression

A binomial expression is an algebraic expression which is having two unlikely terms.

Examples of binomial include 5xy + 8, xyz + x3, etc.

Polynomial Expression

In general, an expression with more than one terms with non-negative integral exponents of a variable is known as a polynomial.

Examples of polynomial expression include ab + bc + ca,  etc.

Other Types of Expression:

Apart from monomial, binomial and polynomial types of expressions, alebraic expression can also be classsified into two additional types which are:

  • Numeric Expression
  • Variable Expression

Numeric Expression:

A numeric expression consists of numbers and operations, but never include any variable. Some of the examples of numeric expressions are 10+5, 15÷2, etc.

Variable Expression:

A variable expression is an expression which contains variables along with numbers and operation to define an expression. A few examples of a variable expression include 4x+y, 5ab + 33, etc.

Algebraic Expression Example Question

Example: Simplify the given expressions by combining the like terms and write the type of Algebraic expression.

(i) 3xy­­3 + 9x2 y3 + 8x3 + 5y3x

(ii) 7ab2 c2 + 2a3 b2 − 3abc – 5ab2 c2 – 2b2 a3 + 2ab

(iii) 50x3 – 20x + 83 + 21x3 – 3x + 3 + 15x – 41x3

Solution: .

Creating a table to find the solution: Term Simplification Type of Expression
1 3xy­­3 + 9x2 y3 + 8x3 + 5y3x 8xy3 + 9x2y3 Binomial
2 7ab2 c2 + 2a3 b2 − 3abc – 5ab2 c2 – 2b2 a3 + 2ab 2ab2 c2 − 3abc + 2ab Trinomial
3 50x3 – 20x + 83 + 21x3 – 3x + 3 + 15x – 41x3 3x³ Monomial

Frequently Asked Questions on Algebraic Expressions

How to derive algebraic expressions?

An algebraic expression is a combination of constant, variables and algebraic operations(+, -, ×, ÷). We can derive the algebraic expression for a given situation or condition by using these combinations.

For example, Sima age is thrice more than Tina. And the total age of Sima and Tina is 40. Expressing the algebraic form of this condition;

3x + x = 40 ⇒ 4x = 40; where x is the age of Tina.

Are algebraic expressions polynomials?

No, not all algebraic expressions are polynomials. But all polynomials are algebraic expressions. The difference is polynomials include only variables and coefficients with mathematical operations(+, -, ×) but algebraic expressions include irrational numbers as well.

Also, polynomials are continuous function(eg: x2 + 2x + 1) but algebraic expression may not be continuous sometimes(eg: 1/x2 – 1 is not continuous at 1).

Is 4 an algebraic expression?

No, 4 is not an algebraic expression because an expression should have at least one variable and one operation to be algebraic.

What are all the types of algebraic expressions?

There are three basic types of algebraic expressions. They are:

  1. Monomial - Which has only one non-zero term.
  2. Binomial - Which has two non-zero terms.
  3. Polynomial - Which has more than one non-zero terms with non-negative integral exponents.