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\begin{center}\section*{\textcolor{red}{TD \no 11 (dÃ©veloppements )}}\end{center}




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\subsection{}
Simplifier $a(b-c)+b(c-a)+c(a-b)$ pour des nombres $a$, $b$ et $c$ quelconques.

\subsection{}
DÃ©velopper les expressions suivantes :

\begin{enumerate}[$A(x)=$]
\item \Distri{0}{3}{7}{5}

\bigskip

\item \Distri{0}{9}{3}{-7}

\bigskip

\item \Distri{0}{-2}{3}{-5}

\bigskip

\item \Distri{1}{1}{2}{3}

\bigskip

\item \Distri{2}{8}{1}{5}

\bigskip

\item \Distri{5}{4}{4}{7}

\bigskip

\item \Distri{7}{-4}{2}{1}

\bigskip

\item \Distri{3}{1}{4}{2}-\Distri{0}{5}{3}{-2}

\bigskip

\item \Distri{5}{-4}{3}{7}-\Distri{4}{-3}{5}{9}
\end{enumerate}

\subsection{}
ComplÃ©ter \dots par des nombres entiers :

\begin{enumerate}[1)]

\bigskip

\item $ (5x+6)(2x+\cdots) = \cdots x^2 +\cdots x+18$

\bigskip

\item $ (4x+3)(x+5) = \cdots x^2 +\cdots x+\cdots $

\bigskip

\item $(2x -\cdots)(3x+4) = \cdots x^2- \cdots x-24$

\bigskip

\item $3x(\cdots x+2)+\cdots x = 12x^2 +11x$


\end{enumerate}

\subsection{}
Rappeler le dÃ©veloppement de :
\begin{enumerate}[$\bullet$]
\item $(a+b)^2$

\item $(a-b)^2$

\item $(a+b)(a-b)$
\end{enumerate}

\subsection{}
DÃ©velopper, en utilisant les identitÃ©s remarquables :

\begin{enumerate}[$A(x)=$]
\item \Distri[Remarquable]{2}{3}{}{}

\bigskip

\item \Distri[Remarquable]{3}{-5}{}{}

\bigskip

\item \Distri[Remarquable]{7}{3}{7}{-3}

\bigskip

\item $\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)$
\end{enumerate}



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