# Algebraic Expressions

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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

8th grade math

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