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Algebraic Expressions

In this section, we shall define an Algebraic Expressions.We shall also define various types of expressions.

A combination of constants and variables connected by the arithmetic signs such as addition (+), subtraction(-), multiplication(x) and division(÷) is called Expressions in algebra.

( Note : Addition (+) and Subtraction(-) separates the term.

Example :

1) 2x
3 +3x 2 -5x +6

This is an expression.

Here we have 4 terms : 2x
3 , 3x 2 , -5x and 6.

2) 3x + 2y - 4z

This is an expression.

Here we have 3 terms : 3x, 2y and -4z.

If the expression contains negative exponents then it is not an expression in algebra.
On the basis of number of terms, there are different types of expressions.

Monomial : An expression containing one term is called Monomial.

For example : 2xy, 5x , -2x, 3x
2 , 10 are all monomials.

Binomial : An expression consisting of 2 terms is a Binomial.

For example : x-y, 2a +b, 2x2 -8.

Trinomial : An expression consisting of 3 terms is called Trinomial.

For example : 3x + 4y -z, 5xy + 4yz + 4 ,a + b –c.

Polynomial : An expression consisting of more than 3 terms is called Polynomial.

For example : 5x +6y -2z +4 , a +2b – c +3d.

Write an expressions for the following :

1) Two more than a.

a + 2

2) The sum of x and 2y.

x + 2y

3) Product of 4 and a.


4) Divide y by 3.

5) Multiply 2 and a and add 5 to the result.

2a + 5

Identify the monomials,binomials, trinomials and polynomials.


This is a monomial expression as it contains one term only.

(ii) x
2 -1

This is a binomial expression as it contains two terms.

(iii) x
2 - y 2

This is a binomial expression as it consists of two terms.

(iv) 3x
2 + 4y 2 + 5z

This is a trinomial as it contains three terms.

Algebraic Expressions

Like and Unlike terms in Algebra
Addition of algebraic-expressions
Subtraction of algebraic-expressions
Multiplication of algebraic-expressions
Division of algebraic-expressions
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