Question

How to factorize by using identity

Answer 1

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 ² + 2ab + b ² , a ² – 2ab + b ² , a ² – b ² and x ² + (a + b) + ab. These expressions can be easily factorized using Identities I, II, III and IV

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

(1) (a + b)² = a² + 2ab +b²,

(2) (a - b)² = a² - 2ab + b² and

(3) a² – b² = (a + b)(a – b).

4) x² + (a + b) x + ab = (x + a) (x + b)


Examples:


(i) 4m² – 12mn + 9n²

Solution:

We can express 4m² – 12mn + 9n² as using a² - 2ab + b² = (a - b)²

= (2m)² - 2(2m)(3n) + (3n)²

= (2m – 3n)²

= (2m - 3n)(2m - 3n)

(ii) 16x² – 36y²

Solution:

We can express 16x² – 36y² as using a² – b² = (a + b)(a - b).

= (4x)² - (6y)²

= (4x + 6y)(4x – 6y)


(iii) 1 – 25(2a – 5b)²

Solution:

We can express 1 – 25(2a – 5b)² as using a² – b² = (a + b)(a - b).

= (1)² - [5(2a – 5b)]²

= [1 + 5(2a – 5b)] [1 - 5(2a – 5b)]

= (1 + 10a – 25b) (1 – 10a + 25b)