Determine the coefficient of \(x^{2}\) in the expansion of \((a + 3x)^{6}\).
FURTHER MATHEMATICS
WAEC 2011
Determine the coefficient of \(x^{2}\) in the expansion of \((a + 3x)^{6}\).
- A. \(18a^{2}\)
- B. \(45a^{4}\)
- C. \(135a^{4}\)
- D. \(1215a^{2}\)
Correct Answer: C. \(135a^{4}\)
Explanation
\((a + 3x)^{6}\).
The coefficient of \(x^{2}\) is:
\(^{6}C_{4}(a)^{6 - 2} (3x)^{2} = \frac{6!}{(6 - 4)! 4!} (a^{4})(9x^{2})\)
\(15 \times a^{4} \times 9 = 135a^{4}\)
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