# Factorization by Grouping

Factorization by Grouping : In factorization all the terms in a given expression do not have a common factor; but the terms can be rearranged in such a way that all the terms in each group have a common factor.

In factorization by regrouping, we should remember that any regrouping of the terms in the given expression may not lead to factorization. We must observe the expression and come out with the desired regrouping by trial and error.

Method of Factorization by Grouping :

1) Rearranging the expression so as to form groups.
2) Find the common factors from each group.

Examples :

1) 2xy + 3 + 2y + 3x

Solution :
2xy + 3 + 2y + 3x

Rearranging the expression, as 2xy + 2y + 3x + 3

=
2xy + 2y + 3x + 3 [these are the two groups]

Common factor from 1st group = 2y

Common factor from 2nd group = 3

= 2y ( x + 1) + 3( x + 1)

Now there are two terms, take common binomial factor (x + 1)

= (x + 1) (2y + 3)

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2) Factorize 6xy – 4y + 6 – 9x.

Solution :
6xy – 4y + 6 – 9x

Rearranging the expression, as 6xy - 9x - 4y + 6

=
6xy - 9x - 4y + 6 [these are the two groups]

Common factor from 1st group = 3x

Common factor from 2nd group = - 2

= 3x( 2y - 3) - 2( 2y - 3)

Now there are two terms, take common binomial factor (2y - 3)

= (2y - 3) (3x - 2)

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3) Factorize : 15pq + 15 + 9q + 25p

Solution :
15pq + 15 + 9q + 25p

=
15pq + 9q + 15 + 25p

= 3q (5p + 3) + 5 (3 + 5p)

= 3q ( 5p + 3) + 5(5p + 3) [ use commutative property for addition]

= (5p + 3)(3q + 5)

Factoring

Factorization by common factor
Factorization by Grouping
Factorization using Identities
Factorization of Cubic Polynomial
Solved Examples on Factorization