Question on Factorisation using identities:

Topic : Factorisation using identities:

Question : Factorise 4y^2 – 12y + 9

Solution :
We know that (a + b)^ 2 = a^2 + 2ab + b^2 …………… (I)
(a – b)^2= a^2 – 2ab + b^2………….. (II)
(a + b) (a – b) = a^2 – b^2………… (III)
let us use these identities for factorisation

Observe 4 y^2 = (2y) 2, 9 = 3^2 and 12y = 2 × 3 × (2y)
Therefore, 4 y^2 – 12y + 9 = (2y)^ 2 – 2 × 3 × (2y) + (3)^2
= (2y – 3)2 (required factorisation)