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: 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