Factorise les expressions suivantes à l'aide du tableau ci-dessous.
$$\begin{tabular}{|c|c|}
\hline
Expression&Factorisation\\
$k\times a+k\times b$&$k\times\big(a+b\big)$\\
\hline
$\rnode{NA}{\color{red}(2x+3)}\rnode{ND}{\psframebox{(2x-1)}}+\rnode{NB}{\color{red}(2x+3)}\rnode{NE}{\psframebox{(3x+2)}}$&$\rnode{NC}{(2x+3)}\times\Big[\rnode{NF}{(2x-1)}+\rnode{NG}{(3x+2)}\Big]$\\
\end{tabular}
$$
\ncbar[linecolor=red,angleA=-90,angleB=90]{->}{NA}{NC}
\nbput{\em facteur commun}
\ncbar[linecolor=red,angleA=-90,angleB=90]{->}{NB}{NC}
\ncarc[linecolor=blue,arcangle=30]{->}{ND}{NF}
\ncarc[linecolor=blue,arcangle=30]{->}{NE}{NG}
\par\vspace{5mm}
$$\Eqalign{
A&=(x+1)(x+2)+(x+1)(2x-3)&B&=(3x-1)(x+2)+(3x-1)(3x+1)\cr
C&=(1-2x)(2x+3)+(1-2x)(3x+2)&D&=(2x+3)(2x-3)-(4-5x)(5x-4)\cr
E&=(3x+1)(x+3)-(3x+1)(2x-1)&F&=(2x+3)(2x-1)-(3x+4)(2x-1)\cr
}$$