## 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: x2 + 5x + 23,  y2 + 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-  x2 + 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 x1/2  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         x2 + 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 + b
12. 5 times a minus b.
5a – b
13. 5 times a divide by b.
5a/b
14. 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