Q3 of 86 Page 56

Factorise the following using appropriate identities.

16x2 + 24xy + 9y2

16x2 can be written as (4x)2


24xy can be written as 2(4x)(3y)


9y2 can be written as (3y)2


⇒ 16x2 + 24xy + 9y2 = (4x)2 + 2(4x)(3y) + (3y)2


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


Here a = 4x and b = 3y


⇒ 16x2 + 24xy + 9y2 = (4x + 3y)2


Therefore 16x2 + 24xy + 9y2 = (4x + 3y) (4x + 3y)


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