Đáp án:
$\begin{array}{l}
a:2018 = b:2019 = c:2020\\
\Rightarrow \frac{a}{{2018}} = \frac{b}{{2019}} = \frac{c}{{2020}}\\
= \frac{{a - b}}{{2018 - 2019}} = \frac{{b - c}}{{2019 - 2020}} = \frac{{c - a}}{{2020 - 2018}}\\
= \frac{{a - b}}{{ - 1}} = \frac{{b - c}}{{ - 1}} = \frac{{c - a}}{2}\\
\Rightarrow \left\{ \begin{array}{l}
a - b = b - c\\
c - a = - 2\left( {a - b} \right)
\end{array} \right.\\
\Rightarrow M = \left( {a - b} \right)\left( {b - c} \right) - {\left( {c - a} \right)^2}\\
M = \left( {a - b} \right).\left( {a - b} \right) - {\left( { - 2\left( {a - b} \right)} \right)^2}\\
= {\left( {a - b} \right)^2} - 4{\left( {a - b} \right)^2}\\
= - 3{\left( {a - b} \right)^2}
\end{array}$
