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3241004551 [841]
3 years ago
8

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

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
7 0
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

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