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=
`(r!)/(k!(r-k)!)`

so

4th term
4-1=3
6 is exponent

6C3
`(3x)^(6-3)(-2y)^3`=

`( (6!)/(3!(6-3)!) )((3x)^3(-8y^3)`=

`( (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`