Find the fourth term in the expansion of \((3x - y)^{6}\).

  • A \(-540x^{3}y^{3}\)
  • B \(-540x^{4}y^{2}\)
  • C \(-27x^{3}y^{3}\)
  • D \(540x^{4}y^{2}\)
waec 2016furthermathematics

The correct answer is A. \(-540x^{3}y^{3}\)

Listing out in order, the terms of this expansion have coefficients: \(^{6}C_{6}, ^{6}C_{5}, ^{6}C_{4}, ^{6}C_{3}, ^{6}C_{2}, ^{6}C_{1}, ^{6}C_{0}\)

The 4th term = \(^{6}C_{3}(3x)^{3}(-y)^{3}  = 20 \times 27x^{3} \times -y^{3}\)

= \(-540x^{3}y^{3}\).

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