Question

11) Using the binomial theorem to find the coefficient of the x^4y^13 term in (3x-y)^17

Answer 1

The binomial theorem states that:

`(x+y)^n=\sum ^n_(k\mathop=0)(n!)/(k!(n-k)!)x^(n-k)y^k`

In this case we have the polynomial

`(3x-y)^(17)`

to get the term:

`x^4y^(13)`

we need k=13, this means that this term will be given as:

`\begin{gathered} (17!)/(13!(17-13)!)(3x)^(17-13)(-y)^(13)=2380(3x)^4(-y)^(13) \\ =2380(81x^4)(-y^(13))^{} \\ =-192780x^4y^(13) \end{gathered}`

Therefore we conclude that the coefficient of the term is -192780