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Like and Unlike Terms

Algebraic Expression I - Concepts

Monomial Expression

Binomial Expression

Trinomial Expression

Framing an Algebraic Expression

Like and Unlike Terms

Addition of Algebraic Expression

Degree of a Term

Finding Value of an Expression

Class - 6th ICSE Subjects

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
A. 2x, 2x,-3x	B. 2x,2x,3x	C. 2x,3x,5x	D. None of these
Right Option : A
View Explanation

Question : 2

Identify the like terms in the expression 2x+3xy+5yz+2yx+8y+6z-3xy
A. 3xy, 2yx,-3xy	B. 2x,2x,3x	C. 2x,3x,5x	D. None of these
Right Option : A
View Explanation

Question : 3

Identify the pair/ pairs of like terms in the given expression $dpi{150} 3x^2y+5xy^2+11xy-8yx^2+11x^2y-13y^2x+5xyz+12xy^2$
A. $3x^2y,11x^2y;and ;5xy^2, -12xy^2$		B. $3x^2y,-8yx^2,11x^2y;and; 5xy^2,-13y^2x,12xy^2$
C. $3x^2y, 11x^2y, -8yx^2; and;5xy^2, -13y^2x-12xy^2; and ; +11xy,-5xyz$		D. None of these
Right Option : B
View Explanation