# 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**_________________________________________________________________

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

a - 21 a b + 14

^{2}

**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]