9. Find the fourth term in the expansion of

Question

(3𝑥 − 𝑦)6
A. −540𝑥3𝑦3
B. −540𝑥4𝑦2
C. 540𝑥3𝑦3
D. −27𝑥3𝑦3

Answer 1

Using the binomial theorem, we know that the fourth term in the expansion of $(3𝑥 − 𝑦)^6$ will be:

$\binom{6}{3}(3𝑥)^3(-𝑦)^3 = 20\times27𝑥^3\times(-𝑦)^3 = -540𝑥^3𝑦^3$

Therefore, the answer is $\boxed{\text{A. }-540𝑥^3𝑦^3}$.