square.tex

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
999^2&=(999^2 - 1) + 1\\
999^2&=(999^2 - 1^2) + 1\\
&=(999-1)(999+1) + 1\\
&=998\cdot 1000 + 1\\
&=998000 + 1\\
&=998001
\end{align*}

\begin{align*}
998^2&=(998^2 - 4) + 4\\
&=(998^2 - 2^2) + 4\\
&=(998-2)(998+2) + 4\\
&=996\cdot 1000 +4\\
&=996000 + 4\\
&=996004
\end{align*}

\begin{align*}
997^2&=(997^2 - 9) + 9\\
&=(997^2 - 3^2) + 9\\
&=(997-3)(997+3) + 9\\
&=994\cdot 1000 + 9\\
&=994000 + 9\\
&=994009
\end{align*}
\end{document}