The factors of ( a2 + 4b2 + 4b – 4ab – 2a – 8 ) are

Correct Option:

A

Given that :- The factors of a2 + 4b2 + 4b – 4ab – 2a – 8
= a2 + 4b2 – 4ab – 2a + 4b – 8
= (a – 2b) 2 – 2(a – 2b) – 8
Let, (a – 2b) = x
∴ The given expression = x2 – 2x – 8
= x2 – 4x + 2x – 8
= x(x – 4) + 2(x – 4)
= (x – 4) (x + 2)
Putting the value of x , we get
∴ a2 + 4b2 + 4b – 4ab – 2a – 8 = (a – 2b – 4) (a – 2b + 2)
Therefore , required answer will be (a – 2b – 4) (a – 2b + 2) .