Factorization by Common Factor

A systematic way of factorizing an expression is the Factorization by Common Factor. It consists of three steps:

(i) Write each term of the expression as a product of irreducible factors.
(ii) Look for and separate the common factors.
(iii) Combine the remaining factors in each term in accordance with the distributive law.

Examples on Factorization by Common Factor method :

1) Factorize : 8x + 8

Solution :
The HCF of 8x and 8 is 8.

8x + 8 = 8 ( x + 1)

Check by expanding your answer



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2) Factorize: 4x
2 - 6xy + 12x

Solution :
The HCF of 4x
2 , 6xy and 12 x is 2x.

4x
2 - 6xy + 12x = 2x ( 2x -3y + 6)

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3)
Factorize: 4x 2 - 6xy + 12x

Solution :
The HCF of 4x
2 , 6xy and 12 x is 2x.

4x
2 - 6xy + 12x = 2x ( 2x -3y + 6)
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3)
Factorize : 35 a 2 - 21 a 2 b + 14 a 2 b 2

Solution :
The HCF of 35 a
2 , 21 a 2 b and 14 a 2 b is 7 a
a - 21 a b + 14
2 = 7 a ( 5 – 3b + 2 b) _________________________________________________________________
Binomial as a common factor

Examples
( a + b )( a + b)


2
= 15 ( x – y ) ( x – y) – 5x ( x – y) – ( x –y )

= ( x – y ) ( – 15y – 1)


2
H.C.F of two terms is 3x(x + y)

= 3x(x + y) [ 5x - 1]