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

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.

$540x^{4}y^{2}$

View answer & explanation

Correct answer is A

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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