What is Factorisation ?
When we factorise an algebraic expression, we write it as a product of factors . Algebraic Expressions like 2x+10, 4x+16, x²+5x etc there factor may be numbers, algebraic variable or algebraic expressions. 




Methods of Factorisation 

1.Method of Common Factor 

2. Method of Regrouping

3. Factorisation using identities

4. Splitting term 


1. Method of Common  factor 
When we factorise any algebraic expression using Common method we take out the common which is Common in all the terms of  that algebraic Expression which we are trying to solve or factorise the factor may be number, variable, algebraic expression . 
Lets understand more by Example 

Example 1:
Factorise the expression : 7x-42 
Solution 

7x-42 
Step 1: write the each term  as a product of irreducible factors


7x=7×x
42=7×3×2

7x-42=(7×x)-(7×3×2)
Step 2: Observe what is common in the expression.
We can observe that 7 is common in both the term of RHS 

Step 3 : Take out which is Common in the expression using distributive law . 


By distributive law 
7×(x- 6) = (7x)-(7×6) = 7(x- 6) 

Hence , the factorise form of 7x-42 is 7(x- 6) .