exo84.tex

\begin{myenumerate}
\item Développe et réduis les expressions suivantes
\end{myenumerate}
\begin{multicols}{3}
$\Eqalign{
A&=\underbrace{2\times(x+3)}_{\rnode{A}{}}-7\cr
A&=\overbrace{\hbox to2cm{\strut\dotfill}}^{\rnode{B}{}}-7\cr
\cr
A&=\hbox to1.25cm{\dotfill}\underbrace{+6-7}_{\rnode{C}{}}\cr
A&=\hbox to1.25cm{\dotfill}\overbrace{\hbox
  to2cm{\strut\dotfill}}^{\rnode{D}{}}\cr
\cr
}$
\nccurve[angleA=-90,angleB=90]{->}{A}{B}\nccurve[angleA=-90,angleB=90]{->}{C}{D}
\par\columnbreak\par
$\Eqalign{
B&=\underbrace{4\times(x+1)}_{\rnode{A}{}}+\underbrace{3\times(x-1)}_{\rnode{E}{}}\cr
B&=\overbrace{\hbox to2cm{\strut\dotfill}}^{\rnode{B}{}}+\big(\overbrace{\hbox to2cm{\strut\dotfill}}^{\rnode{F}{}}\big)\cr
\cr
B&=\hbox to2cm{\dotfill}+\big(\hbox to2cm{\strut\dotfill}\big)\cr
B&=\circlenode{B1}{4x}\hbox to1.25cm{\dotfill}\ovalnode{B2}{+3x}\hbox to1.25cm{\dotfill}\cr
B&=\ovalnode{C1}{\hbox to1.25cm{\strut\dotfill}}\hbox to1.25cm{\dotfill}\cr
}$
\nccurve[angleA=-90,angleB=90]{->}{A}{B}\nccurve[angleA=-45,angleB=135]{->}{E}{F}
\nccurve[angleA=-90,angleB=90]{->}{B1}{C1}\nccurve[angleA=-135,angleB=45]{->}{B2}{C1}
\par\columnbreak\par
$\Eqalign{
C&=\underbrace{2\times(x-1)}_{\rnode{A}{}}-\underbrace{4\times(2-x)}_{\rnode{E}{}}\cr
C&=\overbrace{\hbox to2cm{\strut\dotfill}}^{\rnode{B}{}}-\big(\overbrace{\hbox to2cm{\strut\dotfill}}^{\rnode{F}{}}\big)\cr
\cr
C&=\hbox to2cm{\dotfill}-\big(\hbox to2cm{\strut\dotfill}\big)\cr
C&=\ovalnode{B1}{\strut\ldots}\hbox to2cm{\dotfill}\ovalnode{B2}{\strut\ldots}\cr
C&=\ovalnode{C1}{6x}\hbox to1.25cm{\dotfill}\cr
}$
\nccurve[angleA=-90,angleB=90]{->}{A}{B}\nccurve[angleA=-45,angleB=135]{->}{E}{F}
\nccurve[angleA=-90,angleB=90]{->}{B1}{C1}\nccurve[angleA=-135,angleB=45]{->}{B2}{C1}
\end{multicols}
\begin{myenumerate}
\setcounter{enumi}{1}
\item \`A l'aide des exemples ci-dessus, développe et réduis les
  expressions suivantes :
\[D=3(x-2)+6\kern1cm E=4(x-1)+2(3-x)\kern1cm F=2(3-x)-3(4+x)\]
\end{myenumerate}
\begin{Solution}
  \begin{myenumerate}
    \setcounter{enumi}{1}
    \item $D=3x$; $E=2x+2$; $F=-5x+6$
  \end{myenumerate}
\end{Solution}
%@Commentaire: Exercice donné en correction de devoir. Permet un travail en autonomie.