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)
Correct Answer: Option D
Explanation
((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)