Algebraic Expressions

Algebraic Expressions

Algebraic Expressions

A mathematical statement which is obtained by using mathematical fundamental operation between constants and variables with different powers is called an algebraic expression.


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For example:
-     The sum of 2 and x is 2 + x, where the constant 2 and variable x is connected by ‘+’ sign.
-     So, 2 + x is an algebraic expression.
-     Similarly, other algebraic expressions are 2xy, 3x + 4y, x – y2 + 4 , etc.

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Algebraic Terms

The parts of an algebraic expression separated by ‘+’ or ‘–’ signs are called algebraic terms.

For example:
-     3x + 2y is an algebraic expression, where 3x and 2y are two parts connected by ‘+’ sign. So, 3x and 2y are called the terms of the expression 2x + 3y.

Types of algebraic expression

Algebraic expressions are of different types. They are: Monomial, Binomial, Trinomial and multinomial expressions.

-     Monomial Expression: An algebraic expression which contains only one term is called a monomial expression. For example: 4x, 3x2y, -7xyz2, etc.

-     Binomial Expression: An algebraic expression which contains two terms connected by ‘+’ or ‘–’ is called a binomial expression. For example: a + b, 2a2 – 3abx2, 3x – 4ay2, etc.

-     Trinomial Expression: An algebraic expression which contains three terms connected by ‘+’ or ‘–’ is called a trinomial expression. For example: x + 2y – z, a2 + 2ab + b2, etc.

-     Multinomial Expression: An algebraic expression which contains four or more than four terms connected by ‘+’ or ‘–’ is called a multinomial expression. For example: 2x – 2y + z, x3 – a2 + 2ab – b2 + 7, etc.

Coefficient, base and power

-     Coefficient: A numerical or constant quantity placed before the variable and multiplying it is called the coefficient. For example: In an expression 3x, 3 is called the coefficient of x.

-     Base: An alphabet letter used in algebraic expression is called the base. For example: In an expressioin 3x2, x is the base.

-     Power: The repeatation of the same variable for the required number of times in an algebraic expression is called power. For example: In an expressioin 3x2, 2 is the power of x.

Coefficient, base and power

Like and Unlike Terms

-     Like Terms: The terms are like if the terms have the same base with same power of the variable. For example: 2a, -3a, 4a are like terms. x3, 2x3, -5x3, -3x3 are like terms. similarly 7xy, -3xy, 2xy are like terms.

-     Unlike Terms: The terms are unlike if the terms have the different variables or different powers of the base. For example: x, 2x2, 3x2y, -y are unlike terms. x3, x4, x-3, -x are unlike terms. Similarly xy, 2xz, 3x2y are unlike terms.

Values of Algebraic Expressions

When we substitute the value of a variable in an algebraic expression with a number, the value of the expression is obtained after use of mathematical fundamental operations, it is called the value of the expression.

For example: if x = 2 and y = 3, find the value of 2x – 3x2y.
Here, the given expression = 2x – 3x2y
                                       = 2 × 2 – 3 × 22 × 3
                                       = 4 – 3 × 4 × 3
                                       = 4 – 36
                                       = -32

Workout Examples

Example 1: Write the type of each expression.

a.     4x
b.    2a + 3b
c.     3x2 – 4xy + 2y2
d.    9x3 – 10x2 + 4x – 21
e.     3x3 – 2x2 + 5x + 7xy - 8

Solution: Here,
   a.     4x -------> Monomial
   b.    2a + 3b ---------> Binomial
   c.     3x2 – 4xy + 2y2 ---------> Trinomial
   d.    9x3 – 10x2 + 4x – 21 ----------> Multinomial
   e.     3x3 – 2x2 + 5x + 7xy – 8 ----------> Multinomial

Example 2: Rewrite the following statements in algebraic expressions.

a.     The sum of twice x and 5.
b.    Three times the difference of x and y is less than 3a.
c.     5x is added to the product of b and 7.
d.    One fourth of x is added to 25
e.     7x is divided by 14 and added to product of c and 4.

Solution: Here,
   a.     2x + 5
   b.    3(x – y) < 3a
   c.     5x + 7b
   d.    x/4 +25
   e.     7x/14 +4c

Example 3: Write the terms having:

a.     Base = x, power = 2 and coefficient = 1
b.    Base = x, power = 3 and coefficient = -3
c.     Base = y, power = 5 and coefficient = 4b
d.    Base = z, power = 2 and coefficient = -a

Solution: Here,
   a.     x2
   b.    -3x3
   c.     4by5
   d.    –az2

Example 4: Identify the like and unlike terms of the following expressions:
a.     3x, -2x, 7x
b.    3a2, 3a3, 4a
c.     2(x+y), 3(x+y)3, 9(x+y)2

Solution: Here,
             a.     Like terms
             b.    Unlike terms
             c.     Unlike terms

Example 5: If x = 4 and y = 3, find the value of 2xy + 3y2

Solution: Here,
                        x = 4
                        y = 3
                        2xy + 3y2 = 2 × 4 ×3 + 3 × 32
                                            = 24 + 3 × 9
                                            = 24 + 27
                                            = 51

You can comment your questions or problems regarding the algebraic expressions here.


  1. What is the base in the algebraic expression (3x)2

    1. Base in algebraic expressions is the term of reference. We may consider 3x as the base while simplifying the expression like (3x)^2 × (3x)^3 × (3x)^4 = (3x)^2+3+4 = (3x)^9 = 19683x^9. Or, we may take x as the base after the second step like (3x)^2 × (3x)^3 × (3x)^4 = 9x^2 × 27x^3 × 81x^4 = 9×27×81x^2+3+4 = 19683x^9.