Like and Unlike Terms


 
 
Concept Explanation
 

Like and Unlike Terms

Like Terms:

When terms have the same algebraic factors, they are like terms or we can say like terms are terms that have the same variables and powers. The coefficients can be different so there is no need to match them.

Unlike Terms:

When terms have different algebraic factors they are unlike terms or we can say that Unlike terms are two or more terms that do not have the same variables or powers. The order of the variables does not matter unless they are different.

Factors of a term:

The expression (4x^{2}-3xy)    consists of two terms 4x^{2}  and -3xy.The term 4x^{2}  is a product of 4, x, and x: we say that 4,x, and x are factors of the term 4x^{2}. A term is a product of its factors.

We can represent the terms and factors of the terms of an expression by a tree diagram.

Illustration:  Find the factors of the expression 5xy^{2}+7x^{2}y using a tree diagram.

Solution: The terms and factors of the given expression are shown in the following tree diagram

                  

Illustration:  Find the factors of the expression using a tree diagram.

                       (i)    -3xy+10

                       (iI)     x^{2}+y^{2}

Solution: The terms and factors of the given expression are shown in the following tree diagram

                

                

Illustration:  In the expression 2xy-3x+5xy-4, find terms, factors and identify like and unlike terms.

Solution: In the given expression, terms are 2xy, -3x, 5xy, -4 .

The factors of 2xy are 2,x, and y.

The factors of 5xy are 5,x, and y.

Thus their algebraic factors are the same and hence they are like terms.

On the other hand the terms 2xy and -3x,

The factors of 2xy are 2, x and y

The factors of -3x are -3. x

Thus they have different algebraic factors. They are unlike terms.

Similarly, the terms,2xy and 4, are unlike terms. Also, the terms -3x and 4 are unlike terms.

Illustration: Identify the pair of like terms in the following

(1);8xyz^2;and -5xyz^2

(2);8xy^3z^2 ;and ;5z^2xy^3

(3) ;3abc; and; 3ghi

Solution:

(1);8xyz^2;and -5xyz^2 are like terms because they have the same variables and power,

(2);8xy^3z^2 ;and ;5z^2xy^3  are like terms as the powers are same with respect to the variable even when the order of the variable is different .

(3) ;3abc; and; 3ghi  are unlike terms because they have different variables. Since the coefficient doesn't affect likeness, all constant terms are like terms.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Identify the like terms in the expression 2x+3y+5z+2x+8y+6z-3x

Right Option : A
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Explanation
Question : 2

Identify the like terms in the expression 3xy+11yz+2y+8y+3xy

Right Option : A
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Explanation
Question : 3

Identify the like terms in the expression:

3xy+5yz+2xz+9xy-2z

Right Option : C
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Explanation
 
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