What must be added to 4x\(^2\) - 4 to make it a perfect square?
A
\(\frac{-1}{x^2}\)
B
\(\frac{1}{x^2}\)
C
1
D
-1
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
4x\(^2\) - 4 = (2x)\(^2\) - 2\(^2\)
(2x)\(^2\) - 2\(^2\) = a\(^2\) - b\(^2\) = (a - b)\(^2\) - 2ab - 2b\(^2\)
(a - b)\(^2\) = a - b\(^2\) + (2ab + 2b)\(^2\)
a = 2x and b = 2
2ab + 2b\(^2\) = 2(2x)(2) + 2(2)\(^2\) = 8x + 8 = 8(x + 1)
Source: Myschool Past Questions Archive (Record #31458)