Q3 of 86 Page 56

Factorise the following using appropriate identities.

4y2 - 4y + 1

4y2 can be written as (2y)2


4y can be written as 2(1)(2y)


1 can be written as 12


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


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


Here a = 2y and b = 1


⇒ 4y2 - 4y + 1 = (2y - 1)2


Therefore 4y2 - 4y + 1 = (2y - 1) (2y - 1)


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