Which of the expressions $$(1+x^2-x^3)^{100} \textrm{or}\:\: (1-x^2+x^3)^{100}$$ has the larger coefficient of $x^{20}$ after expending abd and collecting terms.
I can easily do this question via multinomial expansion, but here's the twist. In the question it was written to use the hint given to solve the problem. The hint was replace $-x$ with $x$ to gain extra information.
I replaced, searched for symmetric properties, odd-even properties but couldn't found any. I'm looking for a solution incorporating the above given hint. Also, if there is any method as easy as ABC to do this, I will also appreciate that.