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


= () ()


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