Finding a coefficient of $x^{57}$ in a polynomial $(x^2+x^7+x^9)^{20}$ So the task is to find a coefficient of $x^{57}$ in a polynomial $(x^2+x^7+x^9)^{20}$
I was wondering if there is a more intelligible and less exhausting strategy in finding the coefficient, other than saying that $(x^2+x^7+x^9)^{20}=((x^2+x^7)+x^9)^{20}$ and then working with binomial expansion.

$x^{40}(1+x^5+x^7)^{20}=x^{40}(1+x^5(1+x^2))^{20}=$
$x^{40}(1+20x^5(1+x^2)+$
$(20)(19)/2![(x^5)(1+x^2)]^2+$
$(20)(19)(18)/3![x^5(1+x^2)]^3+..).$
Need the coefficient of  $x^{17}$ in the above expansion.
Which term is relevant?
