Is it possible to simplify the following polynomial? $$T=(a+t_1)+(a+t_1)(a+t_2)+\cdots\prod_{i=1}^n(a+t_i)-(a+a^2+\cdots a^n)$$
What I think: We can first consider a special case when $t_1=t_2=\cdots=t$, then it comes to $T=(a+t)+(a+t)^2+\cdots(a+t)^n-(a+a^2+\cdots a^n)$, but it seems also cannot be reduced.