Factorize by Regrouping The Terms

In factorize by regrouping the terms sometimes it is observed that all the terms of the expression do not have any common factor, neither a monomial nor a binomial.

Follow the steps to factorize by regrouping the terms:  

Step 1: From the algebraic expression arrange the groups of the given expression in such a way, that a common factor can be taken out from each group.

Step 2: Factorize each group.

Step 3: Now take out the common factor of the groups formed.

Examples to factorize algebraic expressions:

1. Factoring the following expressions

(i) ab (x² + y²) - xy (a² + b²)

Solution:

ab(x² + y²) - xy(a² + b²)

By suitably rearranging the terms, we have;

= abx² + aby² - a²xy - b²xy

= abx² - a²xy - b²xy + aby²

= ax(bx - ay) - by(bx - ay)

= (bx - ay) (ax - by)

(ii) 2ax – 4ay - 3bx + 6y    

Solution:    

2ax – 4ay - 3bx + 6y        

By suitably rearranging the terms, we have;                 

= 2ax – 3bx – 4ay + 6by                        

= x(2a – 3b) - 2y(2a – 3b)                   

= (2a – 3b) (x - 2y)

(iii) - 5 - 10t + 20t²

Solution:

- 5 - 10t + 20t²

By suitably rearranging the terms, we have;

= 20t² - 10t - 5

= 5(4t² - 2t - 1)

2. Factorize the expression:

(i) ab – a – b + 1

Solution: 

ab – a – b + 1

By suitably rearranging the terms, we have; 

= ab – b – a + 1

= b(a - 1) - 1(a - 1)

= (a - 1) (b - 1)

(ii) ax + ay - bx – by

Solution: 

ax + ay - bx – by

By suitably rearranging the terms, we have; 

= ax - bx + ay - by

= (ax - bx) + (ay - by)

= x(a - b) + y(a - b)

= (a - b) (x + y)

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8th Grade Math Practice

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