Factorize completely \((x^2 + x)^2 - (2x + 2)^2\)

  • A (x + 1)(x + 2)(x - 2)
  • B (x + 1) 2(x + 2) (x - 2)
  • C (x + 1)2 (x + 2)2
  • D (x + 1)2 (x + 2)(x - 2)
jamb 1988mathematics

The correct answer is D. (x + 1)2 (x + 2)(x - 2)

\((x^{2} + x)^{2} - (2x + 2)^{2}\)

= \((x^{2} + x + 2x + 2)(x^{2} + x - (2x + 2))\)

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

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

= \((x + 1)^{2} (x + 2)(x - 2)\)

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