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: Option A
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}).