Question 1137600
Using the binomial theorem, expand the binomial 

{{{(x + 3)^17 =17C0*x^17*3^0+17C1*x^16*3^1+17C2*x^15*3^2}}}+{{{17C3 (x)^14*(3)^3+17C4 (x)^13*(3)^4+17C5 (x)^12*(3)^5}}}+{{{17C6 (x)^11*(3)^6+17C7 (x)^10*(3)^7 }}}+{{{17C8 (x)^9*(3)^8+17C9 (x)^8*(3)^9+17C10 (x)^7*(3)^10+17C11 (x)^6*(3)^11+17C12 (x)^5*(3)^12+17C13 (x)^4*(3)^13+17C14 (x)^3*(3)^14}}} +{{{ (x)^2*(3)^15 +17C16 (x)^1*(3)^16 +17C17 (x)^103*(3)^17}}}

use term with {{{x^8}}}:

{{{17C9 (x)^8*(3)^9=478493730 x^8}}} => coefficient is {{{478493730}}}