Factorize each of the following algebraic expressions:

It can be written as (a2 – 5a)2 - 62

Using a2 – b2 = (a + b) (a – b)


(a2 – 5a)2 – 62 = (a2 – 5a + 6) (a2 – 5a – 6)


To factorize (a2 – 5a + 6), we need to find p and q where,


p + q = -5, pq = 6


Clearly,


-2 – 3 = -5, (-2) (-3) = 6


Therefore, split -5a as a – 6a


Therefore,


a2 -5a – 6 = a2 - a – 6a + 6


= (a – 6) (a – 1)


Therefore,


(a2 – 5a)2 – 3b = (a2 – 5a + b) (a2 – 5a – 6)


= (a – 1) (a – 2) (a – 3) (a – 6)


12