Question

What is the fourth term of the binomial expansion for (3x-2y)6

Answer 1

One way is to just expand it by using binomial theorem
or to use pascal's triangle

ok so

to find the nth term of a binomial, (a-b). where the binomial is to the r power you do
n-1=k

rCk times $(a)^{r-k}(-b)^k$
and rCk=$\frac{r!}{k!(r-k)!}$

so

4th term
4-1=3
6 is exponent

6C3$(3x)^{6-3}(-2y)^3$=
$( \frac{6!}{3!(6-3)!} )((3x)^3(-8y^3)$=
$( \frac{6*5*4}{1*2*3} )(27x^3)(-8y^3)$=
$(20)(27)(-8)(x^3)(y^3)=-4320x^3y^3$



the 4th term is $-4320x^3y^3$