Factorization by Grouping of Terms


 
 
Concept Explanation
 

Factorization by Grouping of Terms

In order to factorize algebraic expressions containing a binomial as a common factor, we write the expression as the product of the binomial and the quotient obtained by dividing the given expression by this binomial.

Illustration : Factorize:  (y-x)a+(x-y)b

Solution :

 (y-x)a+(x-y)b

=-(x-y)a+(x-y)b      [ Taking (-1) common from (y-x)]

=-(x-y)(-a+b)            [ Taking (x - y) common]

=-(x-y)(b-a)               [because  -a + b = b - a ]

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Sample Questions
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Question : 1

The real factors of x^{2}+4 are:

Right Option : C
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Question : 2

If large 2x^2+xy-3y^2+x+ay-10 = (2x+3y+b)(x-y-2), then the values of a and b are

Right Option : D
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Question : 3

Factorize the following:

large dpi{110} 2x^3y^2-4x^2y^3+8xy^4

Right Option : B
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