WAEC - Further Mathematics (2016 - No. 16)
Find the fourth term in the expansion of \((3x - y)^{6}\).
\(-540x^{3}y^{3}\)
\(-540x^{4}y^{2}\)
\(-27x^{3}y^{3}\)
\(540x^{4}y^{2}\)
Explicació
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 = \(^{6}C_{3}(3x)^{3}(-y)^{3} = 20 \times 27x^{3} \times -y^{3}\)
= \(-540x^{3}y^{3}\).