Introduction to Factorization

Type I-Factorisation by common factor

1. Consider the expression 3x3−15x2+12x.

In all the term, 3x is taken commonly outside.

(3x×x2)+(3x ×−5x)+(3x×4)


2.  Consider the expression 10xy+5x 3y.

Here the term 5xy is common in the expression. 

10xy+5x 3y


Type II-Factorisation by common binomial factor

Consider (n2+1)(m−n)+(m2+1)(m−n).

Take binomial factor from each term commonly outside.

(n2+1)(m−n) +(m2+1)(m−n)


=(m−n)(n 2+m2+2)

Type III-Factorisation by grouping

Consider the expression 3m2 +mn+3mn+n2.

Let us take the common factor for the first two terms separately and take the common factor second two terms separately. 




Type IV-Factorisation using identities

Use the following identities to factorise the expressions.


Type V- Factorisation of expression in Quadratic form

Procedure to factorise the expression

Step 1: Determine the coefficient a,b and c.

Step 2: Calculate the product of a and c. Product =ac and sum =b. Thus the middle coefficient is the sum and extreme product is the product value.

Step 3: Express the middle term as sum of two terms such that the sum satisfies the middle term and the product satisfies the extreme product.

Step 4:  Now group the expression into two factors by taking the common expression outside.

Continue reading to

Join any of the batches using this book

Batch List


Course : CBSE Class 8

Start Date : 09.02.2023

End Date : 01.03.2023

Types of Batch : Live Online Class

Subject M T W T F S S
Mathematics(144 hours) 7:15 PM 7:15 PM 7:15 PM 7:15 PM 7:15 PM - -
class 8 math
Medha Sharma

Course : CBSE Class 8

Start Date : 08.02.2023

End Date : 01.09.2023

Types of Batch : Classroom

Subject M T W T F S S
Mathematics(7 hours) 4:15 PM 4:15 PM 4:15 PM 4:15 PM 4:15 PM 4:15 PM 4:15 PM