The expression is : $$(1-3x+x^2)^{111}$$
I tried treating $$(3x+x^2)$$ as one term to turn it into a binomial expression and expanding it to a few terms to see if i could find some pattern to use binomial properties. But that way the term $$(3x+x^2)$$ was further raised to indices.. So it would have taken hours to expand that particular term as well.. Which ofcourse indicated that i should've approached the problem differently. I am quite new to binomial theorem and combinatorics. So while providing answers please try, also, to provide derivations of the theorems/conclusions you use..
Based on @ Jack D'Aurizio comment
The sum of the coefficients of a polynomial is the polynomial evaluated at $x=1$
$$(1-3+1)^{111}=-1$$