Factorization using Identities :There are some identities and using that the factorization is much easier.

A number of expressions to be factorized are of the form or can be put into the form : a

In this section we will learn Factorization using Identities one by one.

_______________________________________________________________

Factorization using Identities :

In the 1st identity, a

1st and the last term should be perfect square and the middle term is two times the square root of 1st and the last term and the sign of the middle term is positive.

1) 9a

9a

= (3a)

= (3a + 2b)

_______________________________________________________________

2) x

x

= (x

= (x

_______________________________________________________________

In the 2nd identity, a

1st and the last term should be perfect square and the middle term is two times the square root of 1st and the last term and the sign of the middle term is negative.

1) 4p

4p

= (2p)

= (2p - 5q)

_______________________________________________________________

2)1 - 16x

= (1)

= (1 - 8x

_______________________________________________________________

Some quadratic polynomials will be missing the middle term. Often these polynomials are the difference of two squares.

These polynomials come from multiplying the sum and difference of binomials, such as (a+b)(a-b)= a

1) 16x

16x

= (4x)x

= (4x + 3y)(4x - 3y)[ since a = 4x and b = 3y; a

_______________________________________________________________

2) x

x

= (x

= (x

In the 2nd parenthesis(bracket), we can apply the 3rd identity of Factorization again

= (x

a

_______________________________________________________________

Consider x

(a + b)

For example, in x

x

• Factorization by common factor

• Factorization by Grouping

• Factorization using Identities

• Factorization of Cubic Polynomial

• Solved Examples on Factorization

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

Worksheets

Chapterwise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers