Find the co-efficient of $x^3y^3zw^2$ in the expression of $(x-y+2z-2w)^9$. 
Find the co-efficient of $x^3y^3zw^2$ in the expression of $(x-y+2z-2w)^9$.

I have clearly understood how to use the bin theorem for $(a+b)^n$, but am unable to extend the theorem to $4$ terms .

We have $9$ copies of $x-y+2z-2w$. We need to choose $3$ factors for the $x^3$, $3$ factors for the $(-y)^3$, and $1$ factor for the $(2z)$; the remaining two factors will be for the $(-2w)^2$. This produces a term $-8 x^3 y^3 z w^2$.
It remains to count how many ways to make the choices above. This is $\binom{9}{3} \binom{6}{3} \binom{3}{1} = \frac{9!}{3!3!1!2!} = 7! = 5040$. So the coefficient is $5040 \cdot (-8) = -40320$.
