Factorize completely ((x^2 + x)^2 – (2x + 2)^2)

A.
(x + 1)(x + 2)(x – 2) 
B.
(x + 1) 2(x + 2) (x – 2) 
C.
(x + 1)^{2} (x + 2)^{2} 
D.
(x + 1)^{2} (x + 2)(x – 2)
Correct Answer: Option D
Explanation
((x^{2} + x)^{2} – (2x + 2)^{2})
= ((x^{2} + x + 2x + 2)(x^{2} + x – (2x + 2)))
= ((x^{2} + 3x + 2)(x^{2} – x – 2))
= (((x + 1)(x + 2))((x + 1)(x – 2)))
= ((x + 1)^{2} (x + 2)(x – 2))