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)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\((x^{2} + x)^{2} - (2x + 2)^{2}\)
= \((x^{2} + x + 2x + 2)(x^{2} + x - (2x + 2))\)
= \((x^{2} + 3x + 2)(x^{2} - x - 2)\)
= \(((x + 1)(x + 2))((x + 1)(x - 2))\)
= \((x + 1)^{2} (x + 2)(x - 2)\)
Source: Myschool Past Questions Archive (Record #31632)