cosi’ e’ un po’ meglio ma io la ripenserei un attimo…
`\documentclass[a4paper,oneside]{book}
\usepackage{float}
%\usepackage{booktabs} %gestione tabelle di qualità
\usepackage{array}
\usepackage{amsmath}
\usepackage{bm}
\begin{document}
\begin{table}[H]
\begin{align*}
&a & &\begin{tabular}{cc}
a & b \\
c & d
\end{tabular}
\\
&c & &d
\end{align*}
\end{table}
\begin{table}[H]
\centering
\begin{align*}
(a+b)\cdot(c+d) =
&\begin{array}{c|l|c|}
\bm{a}&+ac&+ad\\
\hline
\bm{b}&+bc&+bd\\
\hline
&\bm{c}&\bm{d}\\
\end{array}
=ac+ad+dc+bd \\ \hline
(a+b)\cdot(a-b)=
&\begin{array}{c|l|c|}
\bm{a}&+a^2&-ab\\
\hline
\bm{b}&+ab&-b^2\\
\hline
&\bm{a}&\bm{-b}\\
\end{array}
=a^2+ab-ab-b^2=a^2-b^2 \\ \hline
(a+b)^2=(a+b)\cdot(a+b)=
&\begin{array}{c|l|c|}
%
\phantom{-}\bm{a}&a^2&+ab\\
\hline
\bm{b}&+ab&b^2\\
\hline
&\bm{a}&\bm{b}\\
%
\end{array}
=a^2+b^2+ab+ab=a^2+b^2+2ab \\ \hline
(a-b)^2=(a-b)\cdot(a-b)=
&\begin{array}{c|l|c|}
%
\bm{a}&a^2&-ab\\
\hline
\bm{-b}&-ab&b^2\\
\hline
&\bm{a}&\bm{-b}\\
%
\end{array}
=a^2+b^2-ab-ab=a^2+b^2-2ab
\end{align*}
\caption{prodotti}
\label{tab:prodotti2}
\end{table}
\end{document} `