The binomial theorem states that:
[tex](x+y)^n=\sum ^n_{k\mathop=0}\frac{n!}{k!(n-k)!}x^{n-k}y^k[/tex]
In this case we have the polynomial
[tex](3x-y)^{17}[/tex]
to get the term:
[tex]x^4y^{13}[/tex]
we need k=13, this means that this term will be given as:
[tex]\begin{gathered} \frac{17!}{13!(17-13)!}(3x)^{17-13}(-y)^{13}=2380(3x)^4(-y)^{13} \\ =2380(81x^4)(-y^{13})^{} \\ =-192780x^4y^{13} \end{gathered}[/tex]
Therefore we conclude that the coefficient of the term is -192780
