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Factorise completely the expression

(x+2)2...

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 is D

(x+2)2 - (2x+1)2

= (x2+4x+4)(4x2+4x+1)

= x2 + 4x + 4 - 4 x2 - 4x - 1

= -3 x2 + 3

= 3 - 3 x2

= 3(1 - x2)

= 3(1 + x)(1 - x)