Binomial is a Common Factor

Factorization of algebraic expressions when a binomial is a common factor:

The expression is written as the product of binomial and the quotient obtained by dividing the given expression is by its binomial.

Solved examples when a binomial is a common factor:

1. Factorize the expression (3x + 1)2 – 5(3x + 1)

Solution:

(3x + 1)2 – 5(3x + 1)

The two terms in the above expression are (3x + 1)2 and 5(3x + 1)

= (3x + 1) (3x + 1) – 5(3x + 1)

Here, we observe that the binomial (3x + 1) is common to both the terms.

= (3x + 1) [(3x + 1) – 5]; [taking common (3x + 1)]

= (3x + 1) (3x - 4)

Therefore, (3x + 1) and (3x - 4) are two factors of the given algebraic expression.


2. Factorize the algebraic expression 2a(b - c) + 3(b – c)

Solution: 

2a(b - c) + 3(b – c)       

The two terms in the above expression are 2a(b - c), 3(b – c)

Here, we observe that the binomial (b – c) is common to both the terms, then we get

= 2a(b – c) + 3(b – c)

= (b – c) [2a + 3]; [taking common (b – c)]

Therefore, (b – c) and (2a + 3) are two factors of the given algebraic expression.


3. Factorize the expression (2a – 3b) (x – y) + (3a – 2b) (x – y)        

Solution:   

(2a – 3b) (x – y) + (3a – 2b) (x – y)

The two terms in the above expression are (2a – 3b) (x – y) and (3a – 2b) (x – y)

Here, we observe that the binomial (x – y) is common to both the terms, then we get

= (x – y) [(2a – 3b) + (3a – 2b)]

= (x – y) [(2a – 3b) + (3a – 2b)]

= (x – y) [2a – 3b + 3a – 2b]

= (x – y) [5a - 5b]

Taking common 5, we get

= (x – y) 5(a – b)

= 5(x – y) (a – b)

Therefore, 5, (x – y) and (a – b) are three factors of the given algebraic expression.





8th Grade Math Practice

From Binomial is a Common Factor to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.