Trying to create an area table for integer multiplication

Question

I am trying to create a table like the one below. Is there a way to do this in the tabular environment? Or if there is a better way to do this, please let me know. Thank you in advance!

MWE:

\begin{tabular}{c c c | c}
     & 30 & + & 7  \\\hline
    20 & 600 & & 140  \\
    + & & & \\\hline
    3 & 90 & & 21 \\\hline
\end{tabular}

Answer 1

I must confess I don't understand the meaning of the + symbols in a table devoted to multiplication operations. I therefore omit them from the following solution.

The solution provides two LaTeX macros. The main macro is called \mytab, and it takes four arguments: the two integers in the top row of the tabular environment, and the two integers in the left-hand column. There's also an auxiliary macro called \mply (short for "multiply", I suppose) that performs the multiplication operations.

\documentclass{article}
\usepackage{array}
\newcommand\mply[2]{\the\numexpr#1*#2}
\newcommand\mytab[4]{%
\begingroup
    \renewcommand{\arraystretch}{2}
    \setlength{\tabcolsep}{12pt} % default: 6pt
    \begin{tabular}{| r | r  r|}
    \cline{2-3}
    \multicolumn{1}{c|}{} & #1 & #2  \\
    \hline
    #3 & \mply{#1}{#3} & \mply{#2}{#3}  \\
    #4 & \mply{#1}{#4} & \mply{#2}{#4}  \\
    \hline
    \end{tabular}
\endgroup}

\begin{document}
\mytab{30}{7}{20}{3}

\medskip
\mytab{10}{40}{8}{15}
\end{document}

Answer 2

Here is an MWE. I have defines three \parbox macros with different height and width to fill the cells and align its contents. The multicolumns are for removing line from some of the cells:

\documentclass{article}
\usepackage[table]{xcolor}

\renewcommand{\arraystretch}{1.5}

\newcommand{\pbi}[1]{\parbox[c][0.55cm][c]{1.1cm}{\centering #1}}
\newcommand{\pbii}[1]{\parbox[c][1.1cm][c]{1.1cm}{\centering \textcolor{red}{#1}}}
\newcommand{\pbiii}[1]{\parbox[c][1.1cm][c]{0.55cm}{\centering #1}}

\begin{document}

\begin{tabular}{c|c|c|}
\multicolumn{1}{c}{} & \pbi{30 \hfill  $+$ } & \multicolumn{1}{c}{\pbi{7}}  \\
\cline{2-3}
\pbiii{20 $+$ }&\pbii{600}&  \pbii{140} \\
\hline
\pbiii{3} & \pbii{90} & \pbii{21} \\
\cline{2-3}
\end{tabular}

\end{document}