Question

What is the coefficient of the fourth term in the expansion of (x - y)^6?

Answer 1

If you're aware of the binomial theorem, you have that:
$(x-y)^6=\sum_{k=0}^{6}\binom{6}{6-k}x^k(-1)^{6-k}y^{6-k}$
$(x-y)^6=\sum_{k=0}^{6}\binom{6}{k}x^k(-1)^{k}y^{6-k}$

The fourth term is then the case $k=3$, from which:
$c_{3}=\binom{6}{3}x^3(-1)^3y^3= \frac{6!}{3!(6-3)!} * (-x^3y^3)=- \frac{720}{36}x^3y^3=-20x^3y^3$

Answer 2

Answer:

-20

Step-by-step explanation:

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