81. Determine the sum of the coefficients of the polynomial that results from expanding and combining like terms in the expression $\left(1+x-3 x^{2}\right)^{1965}$.
81. If we expand the expression $\left(1+x-3 x^{2}\right)^{1965}$ and combine like terms, we get a polynomial $a_{0}+a_{1} \cdot x+$ $+a_{2} \cdot x^{2}+a_{3} \cdot x^{3}+\ldots$. Note that the sum of its coefficients is equal to the value of the polynomial at $x=1$

$$
\begin{aligned}
& a_{0}+a_{1} \cdot 1+a_{2} \cdot 1^{2}+a_{3} \cdot 1^{3}+\ldots= \\
&=a_{0}+a_{1}+a_{2}+a_{3}+\ldots
\end{aligned}
$$

Of course, there is no need to actually expand the brackets and combine like terms. It is sufficient to substitute $x=1$ into the original expression

$$
\left(1+1-3 \cdot 1^{2}\right)^{1965}=(-1)^{1965}=-1
$$

Thus, $a_{0}+a_{1}+a_{2}+a_{3}+\ldots=-1$.