Determine the coefficient of \(x^{2}\) in the expansion of \((a + 3x)^{6}\).

  • A \(18a^{2}\)
  • B \(45a^{4}\)
  • C \(135a^{4}\)
  • D \(1215a^{2}\)
waec 2011furthermathematics

The correct answer is C. \(135a^{4}\)

\((a + 3x)^{6}\).

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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