Factorize the following using appropriate identities:

(i)

(ii)

(iii)

(i) 9x² + 6xy + y² = (3x)² + (2 * 3x * y) + y²

Using identity, (a + b)² = a² + 2ab + b²

Here, a = 3x and b = y

9x² + 6xy + y² = (3x)² + (2 * 3 * y) + y²

= (3x + y)²

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

(ii) 4y² - 4y + 1 = (4y)² - (2 * 2y * 1) + 1²

Using identity, (a - b)² = a² - 2ab + b²

Here, a = 2y and b = 1

4y² - 4y + 1 = (2y)² - (2 * 2y * 1) + 1²

= (2y - 1)²

= (2y - 1) (2y - 1)

(iii) Using identity,

a² – b² = (a + b) (a – b)

Here, a = x and b = ()

x² – = x² – ()²

= () ()