Simplify \((1 + 2\sqrt{3})^{2} - (1 - 2\sqrt{3})^{2}\)

  • A 0
  • B \(8\sqrt{3}\)
  • C 13
  • D \(2 - 4\sqrt{3}\)
waec 2010furthermathematics

The correct answer is B. \(8\sqrt{3}\)

\((1 + 2\sqrt{3})^{2} = 1 + 4\sqrt{3} + 12 = 13 + 4\sqrt{3}\)

\((1 - 2\sqrt{3})^{2} = 1 - 4\sqrt{3} + 12 = 13 - 4\sqrt{3}\)

\(13 + 4\sqrt{3} - (13 - 4\sqrt{3}) = 13 + 4\sqrt{3} - 13 + 4\sqrt{3}\)

= \(8\sqrt{3}\)

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