Factorise completely the expression
\((x + 2)^2\) - \((2x + 1)^2\)
A
(3x + 2)(1 - x)
B
(3x + 2)(2x + 1)
C
3\((x + 2)^2\)
D
3(x + 1)(1 - x)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\((x + 2)^2\) - \((2x + 1)^2\)
= \((x^2 + 4x + 4) - (4x^2 + 4x + 1)\)
= \(x^2 \) + 4x + 4 - 4 \(x^2 \) - 4x - 1
= -3 \(x^2 \) + 3
= 3 - 3 \(x^2 \)
= 3(1 - \(x^2 \))
= 3(1 + x)(1 - x)
Source: Myschool Past Questions Archive (Record #49387)