Question

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

Answer 1

-20

Explanation:

i did the usa test prep

Answer 2

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= (6!)/(3!(6-3)!) * (-x^3y^3)=- (720)/(36)x^3y^3=-20x^3y^3`