Find the fourth term in the expansion of \((3x - y)^{6}\).
FURTHER MATHEMATICS
WAEC 2016
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. \(540x^{4}y^{2}\)
Correct Answer: A. \(-540x^{3}y^{3}\)
Explanation
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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