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\titre{Technique: Evaluer et reduire}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Troisième}
\date{Novembre 2016}
%\duree{1 heure}
\sujet{01}
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\newcommand{\lesexos}{%
    \begin{Exo}
    Évaluer les expressions suivantes

    \begin{multicols}{3}
        \begin{enumerate}
            
            
        \item $- x - 5$ en $x = 6$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & - 6 - 5 \\ 
A & = & -6 - 5 \\ 
A & = & -11
                \end{eqnarray*}
            \end{solution}
            
            
        \item $- x + 8$ en $x = 1$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & - 1 + 8 \\ 
A & = & -1 + 8 \\ 
A & = & 7
                \end{eqnarray*}
            \end{solution}
            
        \item $- x + 8$ en $x = 3$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & - 3 + 8 \\ 
A & = & -3 + 8 \\ 
A & = & 5
                \end{eqnarray*}
            \end{solution}

            
            
        \item $-10 x^{  2 } + x - 6$ en $x = 7$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & -10 \times 7^{  2 } + 7 - 6 \\ 
A & = & -10 \times 49 + 7 - 6 \\ 
A & = & -490 + 7 - 6 \\ 
A & = & -483 - 6 \\ 
A & = & -489
                \end{eqnarray*}
            \end{solution}
            
        \item $-10 x^{  2 } + x - 6$ en $x = -5$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & -10 \times ( -5 )^{  2 } - 5 - 6 \\ 
A & = & -10 \times 25 - 5 - 6 \\ 
A & = & -250 - 5 - 6 \\ 
A & = & -255 - 6 \\ 
A & = & -261
                \end{eqnarray*}
            \end{solution}
        
        
        \item $-10 x^{  2 } + x + 10$ en $x = 8$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & -10 \times 8^{  2 } + 8 + 10 \\ 
A & = & -10 \times 64 + 8 + 10 \\ 
A & = & -640 + 8 + 10 \\ 
A & = & -632 + 10 \\ 
A & = & -622
                \end{eqnarray*}
            \end{solution}
            
        
        \item $-7 x ( x - ( -7 ) )$ en $x = -10$
            
        \item $-7 x ( x - ( -7 ) )$ en $x = -10$
            
            
        \item $( 8 x + 7 ) ( -5 - 2 x )$ en $x = -2$
        \end{enumerate}
    \end{multicols}
    \end{Exo}

    \begin{Exo}
        Réduis les expressions suivantes

        \begin{multicols}{3}
            \begin{enumerate}
                
                \item A = $x + 1 + x - 4$
                    \begin{solution}
                        \begin{eqnarray*}
                            A & = & x + 1 + x - 4 \\ 
A & = & x + x + 1 - 4 \\ 
A & = & ( 1 + 1 ) x + 1 - 4 \\ 
A & = & 2 x - 3
                        \end{eqnarray*}
                    \end{solution}
                    
                \item B = $x + 6 + 3 + x - 6$
                    \begin{solution}
                        \begin{eqnarray*}
                            A & = & x + 6 + 3 + x - 6 \\ 
A & = & x + 9 + x - 6 \\ 
A & = & x + x + 9 - 6 \\ 
A & = & ( 1 + 1 ) x + 9 - 6 \\ 
A & = & 2 x + 3
                        \end{eqnarray*}
                    \end{solution}
                    
                \item C = $-3 x + 5 + 5 x$
                    \begin{solution}
                        \begin{eqnarray*}
                            A & = & -3 x + 5 + 5 x \\ 
A & = & -3 x + 5 x + 5 \\ 
A & = & ( -3 + 5 ) x + 5 \\ 
A & = & 2 x + 5
                        \end{eqnarray*}
                    \end{solution}

                    
                \item D = $-4 + 2 x - 10 - 10 x$
                    \begin{solution}
                        \begin{eqnarray*}
                            A & = & -4 + 2 x - 10 - 10 x \\ 
A & = & 2 x - 4 - 10 - 10 x \\ 
A & = & 2 x - 14 - 10 x \\ 
A & = & 2 x - 10 x - 14 \\ 
A & = & ( 2 - 10 ) x - 14 \\ 
A & = & -8 x - 14
                        \end{eqnarray*}
                    \end{solution}
                    
                \item E = $-1 - 8 + 8 x + 6 - 4 x$
                    \begin{solution}
                        \begin{eqnarray*}
                            A & = & -1 - 8 + 8 x + 6 - 4 x \\ 
A & = & -9 + 8 x + 6 - 4 x \\ 
A & = & 8 x - 9 + 6 - 4 x \\ 
A & = & 8 x - 3 - 4 x \\ 
A & = & 8 x - 4 x - 3 \\ 
A & = & ( 8 - 4 ) x - 3 \\ 
A & = & 4 x - 3
                        \end{eqnarray*}
                    \end{solution}
                    
                \item E = $x^{  2 } + 3 + 3 x + 3 - 10 x$
                    \begin{solution}
                        \begin{eqnarray*}
                            A & = & x^{  2 } + 3 + 3 x + 3 - 10 x \\ 
A & = & x^{  2 } + 3 x + 3 + 3 - 10 x \\ 
A & = & x^{  2 } + 3 x + 6 - 10 x \\ 
A & = & x^{  2 } + 3 x - 10 x + 6 \\ 
A & = & x^{  2 } + ( 3 - 10 ) x + 6 \\ 
A & = & x^{  2 } - 7 x + 6
                        \end{eqnarray*}
                    \end{solution}

                    
                \item F = $-6 x^{  2 } + 9 - 2 x - 2 - 6 x$
                    \begin{solution}
                        \begin{eqnarray*}
                            A & = & -6 x^{  2 } + 9 - 2 x - 2 - 6 x \\ 
A & = & -6 x^{  2 } - 2 x + 9 - 2 - 6 x \\ 
A & = & -6 x^{  2 } - 2 x + 7 - 6 x \\ 
A & = & -6 x^{  2 } - 2 x - 6 x + 7 \\ 
A & = & -6 x^{  2 } + ( -2 - 6 ) x + 7 \\ 
A & = & -6 x^{  2 } - 8 x + 7
                        \end{eqnarray*}
                    \end{solution}
                    
                \item G = $3 x^{  2 } + 1 x^{  2 } - 9 x - 9 + 3 x$
                    \begin{solution}
                        \begin{eqnarray*}
                            A & = & 3 x^{  2 } + 1 x^{  2 } - 9 x - 9 + 3 x \\ 
A & = & 3 x^{  2 } + x^{  2 } - 9 x - 9 + 3 x \\ 
A & = & ( 3 + 1 ) x^{  2 } - 9 x - 9 + 3 x \\ 
A & = & 4 x^{  2 } - 9 x - 9 + 3 x \\ 
A & = & 4 x^{  2 } - 9 x + 3 x - 9 \\ 
A & = & 4 x^{  2 } + ( -9 + 3 ) x - 9 \\ 
A & = & 4 x^{  2 } - 6 x - 9
                        \end{eqnarray*}
                    \end{solution}
                    
                \item G = $-2 x^{  2 } + 7 - 6 x - 6 x^{  2 } - 2 x$
                    \begin{solution}
                        \begin{eqnarray*}
                            A & = & -2 x^{  2 } + 7 - 6 x - 6 x^{  2 } - 2 x \\ 
A & = & -2 x^{  2 } - 6 x + 7 - 6 x^{  2 } - 2 x \\ 
A & = & -2 x^{  2 } - 6 x^{  2 } - 6 x + 7 - 2 x \\ 
A & = & ( -2 - 6 ) x^{  2 } - 6 x + 7 - 2 x \\ 
A & = & -8 x^{  2 } - 6 x + 7 - 2 x \\ 
A & = & -8 x^{  2 } - 6 x - 2 x + 7 \\ 
A & = & -8 x^{  2 } + ( -6 - 2 ) x + 7 \\ 
A & = & -8 x^{  2 } - 8 x + 7
                        \end{eqnarray*}
                    \end{solution}
            \end{enumerate}
        \end{multicols}
    \end{Exo}
}

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