# 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.

4a

4) Divide y by 3.

y/3

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

2a + 5

**Identify the monomials,binomials, trinomials and polynomials.**

(i)4x

^{2}

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

• Like and Unlike terms in Algebra

• Addition of algebraic-expressions

• Subtraction of algebraic-expressions

• Multiplication of algebraic-expressions

• Division of algebraic-expressions