ad align non ci avevo pensato
comunque dopo averla vista ho fatto un leggere modifica
`\documentclass[a4paper,oneside]{book}
\usepackage{float}
%\usepackage{booktabs} %gestione tabelle di qualità
\usepackage{array}
\usepackage{amsmath}
\usepackage{bm}
\begin{document}
\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 \\[.6cm] %\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 \\[.6cm] %\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 \\[.6cm] %\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{document}
`
altre modifiche?
grazie
Claudio