Factorize each of the following algebraic expressions:

a² – 3a – 54

In order to factorize the given expression, we find to find two numbers p and q such that:

p + q = -3, pq = -54

Clearly,

6 – 9 = - 3, 6 (-9) = -54

Therefore, split – 3a as 6a – 9a

Therefore,

a² – 3a – 54 = a² + 6a – 9a – 54

= (a - 9) (a + 6)

Therefore,

(a + 7) (a – 10) + 16 = (a – 9) (a + 6)