Simplify \((1 + 2\sqrt{3})^{2} - (1 - 2\sqrt{3})^{2}\)
FURTHER MATHEMATICS
WAEC 2010
Simplify \((1 + 2\sqrt{3})^{2} - (1 - 2\sqrt{3})^{2}\)
- A. 0
- B. \(8\sqrt{3}\)
- C. 13
- D. \(2 - 4\sqrt{3}\)
Correct Answer: B. \(8\sqrt{3}\)
Explanation
\((1 + 2\sqrt{3})^{2} = 1 + 4\sqrt{3} + 12 = 13 + 4\sqrt{3}\)
\((1 - 2\sqrt{3})^{2} = 1 - 4\sqrt{3} + 12 = 13 - 4\sqrt{3}\)
\(13 + 4\sqrt{3} - (13 - 4\sqrt{3}) = 13 + 4\sqrt{3} - 13 + 4\sqrt{3}\)
= \(8\sqrt{3}\)
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