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)
waec 2018mathematics

The correct answer is D. 3(x + 1)(1 - x)

\((x + 2)^2\) - \((2x + 1)^2\)

= \((x^2 + 4x + 4) - (4x^2 + 4x + 1)\)

= \(x^2 \) + 4x + 4 - 4 \(x^2 \) - 4x - 1

= -3 \(x^2 \) + 3

= 3 - 3 \(x^2 \)

= 3(1 - \(x^2 \))

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

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