\(\left(x+2018\right)^{2020}-\left(x+2018\right)^{2019}=0\)
\(\Leftrightarrow\) \(\left(x+2018\right)^{2019}\left(x+2018-1\right)=0\)
\(\Leftrightarrow\) \(\left(x+2018\right)^{2019}\left(x+2017\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x+2018\right)^{2019}=0\\x+2017=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2018\\x=-2017\end{matrix}\right.\)
\(\left(x+2018\right)^{2020}-\left(x+2018\right)^{2019}=0\\ \Leftrightarrow\left(x+2018\right)^{2019}\left[\left(x+2018\right)^2-1\right]=0\\ \Leftrightarrow\left(x+2018\right)^{2019}\left(x+2017\right)\left(x+2019\right)=0\\ \Rightarrow\left[{}\begin{matrix}x+2018=0\\x+2017=0\\x+2019=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-2018\\x=-2017\\x=-2019\end{matrix}\right.\)
