<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[11pt] {article} \usepackage[T1]{fontenc} 
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\renewcommand{\thesubsection}{\textcolor{blue}{Exercice \Roman{subsection}}} 
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      \newtheorem{solution}{Solution}

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\begin{document}
%\tableofcontents

\begin{center}\section*{\textcolor{red}{Correction du contrÃ´le sur les dÃ©veloppements}}\end{center}

Remarque : le corrigÃ© ci-dessous est dÃ©taillÃ© ; il faut apprendre Ã&nbsp; dÃ©velopper en appliquant directement la rÃ¨gle des signes.

La rÃ¨gle essentielle est la double distributivitÃ© :
\begin{center}
\Distri[Cours,Fleche]{2}{3}{4}{5}
\end{center}


\begin{multicols}{2}
\setlength{\columnseprule}{1pt}
\setlength{\columnsep}{2 cm}

\subsection{}
\begin{align*}
f(x)&amp;=(5-5x)(7x-5)\\
&amp;=5\times 7x-5\times 5-5x\times 7x+5x\times 5\\
&amp;=35x-25-35x^2+25x\\
&amp;\boxed{\textcolor{red}{-35x^2+60x-25}}
\end{align*}

\subsection{}
\begin{align*}
f(x)&amp; =(1-7x)(5x-6)\\
&amp;=5x-6-35x^2+42x\\
&amp;=\boxed{\textcolor{red}{-35x^2+ 47x-6}}.
\end{align*}

\subsection{}


%\begin{solution}
%$f(x) = (-10x-8)(4-7x)=-40x+70x^2-32+56x=\boxed{\textcolor{red}{70x^2+ 16x-32}}.$
%\end{solution}
\begin{align*}
f(x)&amp;=\Distri{-10}{-8}{4}{-7}\\
f(x)&amp;=\Distri[AideMul]{-10}{-8}{4}{-7}\\
f(x)&amp;=\Distri[AideMul,AideAdda,AideAddb]{-10}{-8}{4}{-7}\\
\\
f(x)&amp;=\Distri[Fleches,CouleurFH=orange,CouleurFB=black,AideMul,AideAdda,AideAddb]{-10}{-8}{4}{-7}\\
\\
f(x)&amp;=\Distri[Etape=2]{-10}{-8}{4}{-7}\\
f(x)&amp;=\Distri[Etape=3,CouleurReduction=purple,Reduction]{-10}{-8}{4}{-7}\\
f(x)&amp;=\boxed{\textcolor{red}{\Distri[Etape=4]{-10}{-8}{4}{-7}}}
\end{align*}


\subsection{}
%\begin{solution}
%$f(x) = (2x-9)(9x+ 1)=18x^2+2x-81x-9=\boxed{\textcolor{red}{18x^2-79x-9}}.$
%\end{solution}
\begin{align*}
f(x)&amp;=\Distri{2}{-9}{9}{1}\\
f(x)&amp;=\Distri[AideMul]{2}{-9}{9}{1}\\
f(x)&amp;=\Distri[AideMul,AideAdda,AideAddb]{2}{-9}{9}{1}\\
\\
f(x)&amp;=\Distri[Fleches,CouleurFH=orange,CouleurFB=black,AideMul,AideAdda,AideAddb]{2}{-9}{9}{1}\\
\\
f(x)&amp;=\Distri[Etape=2]{2}{-9}{9}{1}\\
f(x)&amp;=\Distri[Etape=3,CouleurReduction=purple,Reduction]{2}{-9}{9}{1}\\
f(x)&amp;=\boxed{\textcolor{red}{\Distri[Etape=4]{2}{-9}{9}{1}}}
\end{align*}


\subsection{}


\begin{align*}
f(x)&amp; =(3-5x)(7x+ 8)\\
&amp;=21x+24-35x^2-40x\\
&amp;=\boxed{\textcolor{red}{-35x^2-19x+ 24}}.
\end{align*}


\end{multicols}



\label{fin}
\end{document}  </pre></body></html>