
Pour développer $(a+b+c)^2$, on peut voir ce calcul sous la forme:
\begin{align*}
(a+b+c)^2 & = (\textcolor{red}{a+b}+\textcolor{green}{c})(a+b+c)\\
& = \big[(\textcolor{red}{a+b})(\textcolor{blue}{a+b}+\textcolor{orange}{c})\big] + \textcolor{green}{c}(a+b+c)\\
& = \big[\textcolor{red}{(a+b)}\textcolor{blue}{(a+b)}+ \textcolor{orange}{c}\textcolor{red}{(a+b)}\big] + \textcolor{green}{c}(a+b+c)\\
& = a^2+2ab+b^2 + ac+bc + ac+bc+c^2\\
\Aboxed{(a+b+c)^2 & = a^2+b^2+c^2+2ab+2ac+2bc}
\end{align*}
