# Polynomials

## Exercise 2.5 Part 3

Question 3: Factorise the following using appropriate identities:

(i) 9x^2 + 6xy + y^2

Solution:

Given, 9x^2 + 6xy + y^2

= (3x)^2 + 2 × 3x × y + y^2

Let, a = 3x and b = y

[Using identity, (a + b) ^2 = a^2 + 2ab + b^2]

= (3x + y)^2

= (3x + y)(3x +y) Answer

This can also be solved as follows:

9x^2 + 6xy + y^2

= 9x^2 + 3xy + 3xy + y^2

= 3x(3x + y) + y(3x + y)

= (3x + y)(3x + y)

(ii) 4y^2 - 4y + 1

Solution:

Given, 4y^2 - 4y + 1

= (2y)^2 - 2xx2yxx1 + 1^2

Let, a = 2y and b = 1

[Using identity, (a – b)^2 = a^2 - 2ab +b^2]

= (2y – 1) ^2

= (2y – 1)(2y – 1) Answer

(iii) x^2-(y^2)/(100)

Solution: Given: x^2-(y^2)/(100)

=x^2-(y/10)^2

Let, a = x and b = y/10

(Using identity (a^2-b^2)=(a+b)(a-b))

The polynomial can be written as follows:

=(x+y/10)(x-y/10)