# Variables and Algebraic Expressions – Definition & Example – Algebra

**Variables and Algebraic Expressions**

**Definition: Variable**

**Variables are symbol or letters that used to represent for unknown numbers or values. simply a single letter, that represents a number called the value of the variable.**

**Example: The letters a, b, c, x, y, z, m, p, q are most commonly used for variables.**

**In algebra the letters i and e have special values and are usually not used as a variable, and also the letter o is usually not used because it can be mistaken for 0(zero).**

**Algebraic Expressions**

**An Algebraic Expressions is combination of constants and variables along with operations addition, subtraction, multiplication and division (+, -, x, ÷).**

**3x + 4y – 7z is an algebraic expression.**

**In the algebraic expression 3x + 4y – 7z, 3x, 4y and 7z are called the terms of the expression.**

**Classification of algebraic expressions**

**Monomial-** **An algebraic expression have only one term is called monomial.**

example: 3, 6x, 2y etc. have only one term.

**Binomial- An algebraic expression have two terms is called binomial.**

example: 3 + 5y, 6x – 7z, etc. have only two terms.

**Trinomial-** **An** **algebraic expression have three terms is called trinomial.**

example: 4x + 3 – 6x, 3p +2y +6q etc. have only three terms.

**Multinomial-** **An algebraic expression have more than one term is called multinomial.**

example: x^{2} + 5x + 23, y^{2} + 3x + 2 etc.

**Polynomial-** **If in an algebraic expression the power of variables is a non negative integer, then the expression is called a polynomial.**

example- x^{2} + 5/x is not a polynomial because the power of x in 5/x is negative that is 5/x = 5x^{-1}

2x – √x is not a polynomial because the power of x in √x is x^{1/2} that is a fraction.

**Classification of polynomials on the basis of number of terms.**

Number of terms Polynomial Example

a. 1 Monomial 4, 5x, etc

b. 2 Binomial 2x + 5, x – 2y

c. 3 Trinomial x^{2} + 3x + 2

Following are examples of algebraic expressions with **sign and symbols.**

**1. Sum of a and b.**

a + b

**2. Subtraction of p and q.**

p – q

**3. Product of m and n.**

m x n

**4. Division of s and t.**

s ÷ t

**5. Half of the product of p and q.**

(pq)/2

**6. One fourth of the product of p and q.**

(pq)/4

**7. Sum of 3y and 4x.**

3y + 4x

**8. Value of a is greater then b.**

a > b

**9. Value of a is less then b.**

a < b

**10. Value of a is equal to b.**

a = b

**11. 5 times a plus b.5a + b12. 5 times a minus b.5a – b13. 5 times a divide by b.5a/b14. 5 times a multiply by b.5a x b**

Following are examples of algebraic expressions in **words.**

1. 9x

9 times of x

2. m +n

Sum of m and n

3. p/q

Division of p and q

4. m/3

One third part of m

5. p + q > 8

Sum of p and q is less than 8

6. p + q < 8

Sum of p and q is greater than 8

7. p + q + 8

Sum of p and q and 8

8. pq/8

product of p and q divided by 8

9. (x + 3y)/5

1/5 of sum of x and 3 times y

10. 6m + n

Sum of n and 6 times m