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      \newtheorem{solution}{Solution}

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\begin{document}
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\begin{center}\section*{\textcolor{red}{Correction du contrôle sur les développements}}\end{center}


\begin{solution}
$f(x) =(5-5x)(7x-5)=35x-25-35x^2+25x=\boxed{\textcolor{red}{-35x^2+ 60x-25}}.$
\end{solution}

\begin{solution}
$f(x) =(1-7x)(5x-6)=5x-6-35x^2+42x=\boxed{\textcolor{red}{-35x^2+ 47x-6}}.$
\end{solution}

\begin{solution}
$f(x) = (-10x-8)(4-7x)=-40x+70x^2-32+56x=\boxed{\textcolor{red}{70x^2+ 16x-32}}.$
\end{solution}

\begin{solution}
$f(x) = (2x-9)(9x+ 1)=18x^2+2x-81x-9=\boxed{\textcolor{red}{18x^2-79x-9}}.$
\end{solution}

\begin{solution}
$f(x) =(3-5x)(7x+ 8)=21x+24-35x^2-40x=\boxed{\textcolor{red}{-35x^2-19x+ 24}}.$
\end{solution}

\begin{solution}
$f(x) = (-2x-2)(10x-10)=-20x^2+20x-20x+20=\boxed{\textcolor{red}{ 20-20x^2}}.$
\end{solution}

\begin{solution}
$f(x) =(-3x-9)(4x+ 4)=-12x^2-12x-36x-36=\boxed{\textcolor{red}{-12x^2-48x-36}}.$
\end{solution}

\begin{solution}
$f(x) = (7x+ 2)(8x-1)=56x^2-7x+16x-2=\boxed{\textcolor{red}{56x^2+ 9x-2}}.$
\end{solution}

\begin{solution}
$f(x) =(2-2x)(x+ 5)=2x+10-2x^2-10x=\boxed{\textcolor{red}{-2x^2-8x+ 10}}.$
\end{solution}

\begin{solution}
$f(x) =(-2x-10)(6x+ 2)=-12x^2-4x-60x-20=\boxed{\textcolor{red}{-12x^2-64x-20}}.$
\end{solution}

\label{fin}
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