Question

Factorize each of the following algebraic expressions:

(a² - 5a)² - 36

Answer 1

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)