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 [tex](a)^{r-k}(-b)^k[/tex]
and rCk=[tex] \frac{r!}{k!(r-k)!} [/tex]
so
4th term
4-1=3
6 is exponent
6C3[tex](3x)^{6-3}(-2y)^3[/tex]=
[tex]( \frac{6!}{3!(6-3)!} )((3x)^3(-8y^3)[/tex]=
[tex]( \frac{6*5*4}{1*2*3} )(27x^3)(-8y^3)[/tex]=
[tex](20)(27)(-8)(x^3)(y^3)=-4320x^3y^3[/tex]
the 4th term is [tex]-4320x^3y^3[/tex]
