\documentclass[a5paper,10pt, table]{/media/documents/Cours/Prof/Enseignements/tools/style/classDS}
\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
%\geometry{left=10mm,right=10mm, top=10mm, bottom=10mm}

% Title Page
\titre{Developper et reduire}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Troisième}
\date{Janvier 2016}
%\duree{1 heure}
\sujet{1}
% DS DSCorr DM DMCorr Corr
\typedoc{DM}

\geometry{left=10mm,right=10mm, bottom= 10mm, top=10mm}
\printanswers

\pagestyle{empty}

\begin{document}

\begin{questions}

    \question
    Reduire les expressions suivantes.
        \begin{parts}

            \part $A = 3 x + 6 x + 8 + 5 x$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & 3 x + 6 x + 8 + 5 x \\ 
                    A & = & ( 3 + 6 ) x + 8 + 5 x \\ 
                    A & = & 9 x + 8 + 5 x \\ 
                    A & = & ( 9 + 5 ) x + 8 \\ 
                    A & = & 14 x + 8
                \end{eqnarray*}
            \end{solution}


            \part $B = 5 + 9 x + 2 + 7 x + 9$
            \begin{solution}
                \begin{eqnarray*}
                    B & = & 5 + 9 x + 2 + 7 x + 9 \\ 
                    B & = & 9 x + 5 + 2 + 7 x + 9 \\ 
                    B & = & 9 x + 7 + 7 x + 9 \\ 
                    B & = & ( 9 + 7 ) x + 7 + 9 \\ 
                    B & = & 16 x + 7 + 9 \\ 
                    B & = & 16 x + 16
                \end{eqnarray*}
            \end{solution}


            \part $C = 1 x + 7 x - 6 + 3 x$
            \begin{solution}
                \begin{eqnarray*}
                    C & = & 1 x + 7 x - 6 + 3 x \\ 
                    C & = & x + 7 x - 6 + 3 x \\ 
                    C & = & ( 1 + 7 ) x - 6 + 3 x \\ 
                    C & = & 8 x - 6 + 3 x \\ 
                    C & = & ( 8 + 3 ) x - 6 \\ 
                    C & = & 11 x - 6
                \end{eqnarray*}
            \end{solution}


            \part $D = -4 + 9 x - 9 - 8 x - 2$
            \begin{solution}
                \begin{eqnarray*}
                    D & = & -4 + 9 x - 9 - 8 x - 2 \\ 
                    D & = & 9 x - 4 - 9 -  8 x - 2 \\ 
                    D & = & 9 x - 13 -  8 x - 2 \\ 
                    D & = & ( 9 - 8 ) x - 13 - 2 \\ 
                    D & = & x - 13 - 2 \\ 
                    D & = & x - 15
                \end{eqnarray*}
            \end{solution}


            \part $E = 9 x \times 5 + 8 + 10$
            \begin{solution}
                \begin{eqnarray*}
                    E & = & 9 x \times 5 + 8 + 10 \\ 
                    E & = & 9 \times 5 x + 8 + 10 \\ 
                    E & = & 45 x + 8 + 10 \\ 
                    E & = & 45 x + 18
                \end{eqnarray*}
            \end{solution}


            \part $F = 9 x \times 6 x + 3 + 6 x + 8$
            \begin{solution}
                \begin{eqnarray*}
                    F & = & 9 x \times 6 x + 3 + 6 x + 8 \\ 
                    F & = & 9 \times 6 x x + 3 + 6 x + 8 \\ 
                    F & = & 54 x x + 3 + 6 x + 8 \\ 
                    F & = & 54 x^{  2 } + 3 + 6 x + 8 \\ 
                    F & = & 54 x^{  2 } + 6 x + 3 + 8 \\ 
                    F & = & 54 x^{  2 } + 6 x + 11
                \end{eqnarray*}
            \end{solution}


            \part $G = -8 x \times ( -2 ) - 4 \times ( -2 ) - 4$
            \begin{solution}
                \begin{eqnarray*}
                    G & = & -8 x \times ( -2 ) - 4 \times ( -2 ) - 4 \\ 
                    G & = & - 8 x \times ( -2 ) + 8 - 4 \\ 
                    G & = & -8 \times ( -2 ) x + 8 - 4 \\ 
                    G & = & 16 x + 8 - 4 \\ 
                    G & = & 16 x + 4
                \end{eqnarray*}
            \end{solution}


            \part $H = 7 x \times 2 x + 10 + 7 x + 3 \times 3$
            \begin{solution}
                \begin{eqnarray*}
                    H & = & 7 x \times 2 x + 10 + 7 x + 3 \times 3 \\ 
                    H & = & 7 x \times 2 x + 10 + 7 x + 9 \\ 
                    H & = & 7 \times 2 x x + 10 + 7 x + 9 \\ 
                    H & = & 14 x x + 10 + 7 x + 9 \\ 
                    H & = & 14 x^{  2 } + 10 + 7 x + 9 \\ 
                    H & = & 14 x^{  2 } + 7 x + 10 + 9 \\ 
                    H & = & 14 x^{  2 } + 7 x + 19
                \end{eqnarray*}
            \end{solution}
        \end{parts}

    \question
    Developper et reduire les expressions suivantes.
        \begin{parts}

            \part $A = 5 ( 8 x + 7 )$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & 5 ( 8 x + 7 ) \\ 
                    A & = & 5 \times 8 x + 5 \times 7 \\ 
                    A & = & 40 x + 35
                \end{eqnarray*}
            \end{solution}


            \part $B = 9 ( -6 x + 9 )$
            \begin{solution}
                \begin{eqnarray*}
                    B & = & 9 ( -6 x + 9 ) \\ 
                    B & = & 9 \times ( -6 ) x + 9 \times 9 \\ 
                    B & = & - 54 x + 81
                \end{eqnarray*}
            \end{solution}


            \part $C = 4 x ( 2 x - 7 )$
            \begin{solution}
                \begin{eqnarray*}
                    C & = & 4 x ( 2 x - 7 ) \\ 
                    C & = & 4 \times 2 x^{  2 } + 4 \times ( -7 ) x \\ 
                    C & = & 8 x^{  2 } - 28 x
                \end{eqnarray*}
            \end{solution}


            \part $D = 4 x ( -2 x + 9 )$
            \begin{solution}
                \begin{eqnarray*}
                    D & = & 4 x ( -2 x + 9 ) \\ 
                    D & = & 4 \times ( -2 ) x^{  2 } + 4 \times 9 x \\ 
                    D & = & - 8 x^{  2 } + 36 x
                \end{eqnarray*}
            \end{solution}


            \part $E = -7 ( -9 x + 6 ) + 2$
            \begin{solution}
                \begin{eqnarray*}
                    E & = & -7 ( -9 x + 6 ) + 2 \\ 
                    E & = & -7 \times ( -9 ) x - 7 \times 6 + 2 \\ 
                    E & = & 63 x - 42 + 2 \\ 
                    E & = & 63 x - 40
                \end{eqnarray*}
            \end{solution}


            \part $F = -4 x ( -1 x + 3 ) + 3$
            \begin{solution}
                \begin{eqnarray*}
                    F & = & -4 x ( -1 x + 3 ) + 3 \\ 
                    F & = & - 4 x ( - x + 3 ) + 3 \\ 
                    F & = & -4 \times ( -1 ) x^{  2 } - 4 \times 3 x + 3 \\ 
                    F & = & 4 x^{  2 } - 12 x + 3
                \end{eqnarray*}
            \end{solution}
        \end{parts}

    \question
    Developper et reduire les expressions suivantes.
        \begin{parts}

            \part $A = ( 1 x - 9 ) ( 1 x + 7 )$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & ( 1 x - 9 ) ( 1 x + 7 ) \\ 
                    A & = & ( x - 9 ) ( x + 7 ) \\ 
                    A & = & x^{  2 } + ( -9 + 7 ) x - 9 \times 7 \\ 
                    A & = & x^{  2 } - 2 x - 63
                \end{eqnarray*}
            \end{solution}


            \part $B = ( 4 x + 5 ) ( 10 x - 2 )$
            \begin{solution}
                \begin{eqnarray*}
                    B & = & ( 4 x + 5 ) ( 10 x - 2 ) \\ 
                    B & = & 4 \times 10 x^{  2 } + ( 5 \times 10 + 4 \times ( -2 ) ) x + 5 \times ( -2 ) \\ 
                    B & = & 40 x^{  2 } + ( 50 - 8 ) x - 10 \\ 
                    B & = & 40 x^{  2 } + 42 x - 10
                \end{eqnarray*}
            \end{solution}


            \part $C = ( -6 x - 9 ) ( -10 x - 7 )$
            \begin{solution}
                \begin{eqnarray*}
                    C & = & ( -6 x - 9 ) ( -10 x - 7 ) \\ 
                    C & = & -6 \times ( -10 ) x^{  2 } + ( -9 \times ( -10 ) - 6 \times ( -7 ) ) x - 9 \times ( -7 ) \\ 
                    C & = & 60 x^{  2 } + ( 90 + 42 ) x + 63 \\ 
                    C & = & 60 x^{  2 } + 132 x + 63
                \end{eqnarray*}
            \end{solution}


            \part $D = ( -5 x + 2 ) ( -8 x + 6 )$
            \begin{solution}
                \begin{eqnarray*}
                    D & = & ( -5 x + 2 ) ( -8 x + 6 ) \\ 
                    D & = & -5 \times ( -8 ) x^{  2 } + ( 2 \times ( -8 ) - 5 \times 6 ) x + 2 \times 6 \\ 
                    D & = & 40 x^{  2 } + ( -16 - 30 ) x + 12 \\ 
                    D & = & 40 x^{  2 } - 46 x + 12
                \end{eqnarray*}
            \end{solution}


            \part $E = ( -6 x + 2 ) ( 2 x + 5 )$
            \begin{solution}
                \begin{eqnarray*}
                    E & = & ( -6 x + 2 ) ( 2 x + 5 ) \\ 
                    E & = & -6 \times 2 x^{  2 } + ( 2 \times 2 - 6 \times 5 ) x + 2 \times 5 \\ 
                    E & = & - 12 x^{  2 } + ( 4 - 30 ) x + 10 \\ 
                    E & = & - 12 x^{  2 } - 26 x + 10
                \end{eqnarray*}
            \end{solution}


            \part $F = ( 1 x - 4 ) ( 9 x + 10 )$
            \begin{solution}
                \begin{eqnarray*}
                    F & = & ( 1 x - 4 ) ( 9 x + 10 ) \\ 
                    F & = & ( x - 4 ) ( 9 x + 10 ) \\ 
                    F & = & 9 x^{  2 } + ( -4 \times 9 + 10 ) x - 4 \times 10 \\ 
                    F & = & 9 x^{  2 } + ( -36 + 10 ) x - 40 \\ 
                    F & = & 9 x^{  2 } - 26 x - 40
                \end{eqnarray*}
            \end{solution}
        \end{parts}

    \question
    Developper et reduire les expressions suivantes.
        \begin{parts}

            \part $A = ( 3 x + 4 )^{  2 }$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & ( 3 x + 4 )^{  2 } \\ 
                    A & = & ( 3 x + 4 ) ( 3 x + 4 ) \\ 
                    A & = & 3 \times 3 x^{  2 } + ( 4 \times 3 + 3 \times 4 ) x + 4 \times 4 \\ 
                    A & = & 9 x^{  2 } + ( 12 + 12 ) x + 16 \\ 
                    A & = & 9 x^{  2 } + 24 x + 16
                \end{eqnarray*}
            \end{solution}


            \part $B = ( 10 x + 8 )^{  2 }$
            \begin{solution}
                \begin{eqnarray*}
                    B & = & ( 10 x + 8 )^{  2 } \\ 
                    B & = & ( 10 x + 8 ) ( 10 x + 8 ) \\ 
                    B & = & 10 \times 10 x^{  2 } + ( 8 \times 10 + 10 \times 8 ) x + 8 \times 8 \\ 
                    B & = & 100 x^{  2 } + ( 80 + 80 ) x + 64 \\ 
                    B & = & 100 x^{  2 } + 160 x + 64
                \end{eqnarray*}
            \end{solution}


            \part $C = ( 6 x - 6 )^{  2 }$
            \begin{solution}
                \begin{eqnarray*}
                    C & = & ( 6 x - 6 )^{  2 } \\ 
                    C & = & ( 6 x - 6 ) ( 6 x - 6 ) \\ 
                    C & = & 6 \times 6 x^{  2 } + ( -6 \times 6 + 6 \times ( -6 ) ) x - 6 \times ( -6 ) \\ 
                    C & = & 36 x^{  2 } + ( -36 - 36 ) x + 36 \\ 
                    C & = & 36 x^{  2 } - 72 x + 36
                \end{eqnarray*}
            \end{solution}


            \part $D = ( 9 x - 10 )^{  2 }$
            \begin{solution}
                \begin{eqnarray*}
                    D & = & ( 9 x - 10 )^{  2 } \\ 
                    D & = & ( 9 x - 10 ) ( 9 x - 10 ) \\ 
                    D & = & 9 \times 9 x^{  2 } + ( -10 \times 9 + 9 \times ( -10 ) ) x - 10 \times ( -10 ) \\ 
                    D & = & 81 x^{  2 } + ( -90 - 90 ) x + 100 \\ 
                    D & = & 81 x^{  2 } - 180 x + 100
                \end{eqnarray*}
            \end{solution}


            \part $E = ( 2 x + 6 ) ( 2 x - 6 )$
            \begin{solution}
                \begin{eqnarray*}
                    E & = & ( 2 x + 6 ) ( 2 x - 6 ) \\ 
                    E & = & 2 \times 2 x^{  2 } + ( 6 \times 2 + 2 \times ( -6 ) ) x + 6 \times ( -6 ) \\ 
                    E & = & 4 x^{  2 } + ( 12 - 12 ) x - 36 \\ 
                    E & = & 4 x^{  2 } - 36
                \end{eqnarray*}
            \end{solution}


            \part $F = ( 8 x + 10 ) ( 8 x - 10 )$
            \begin{solution}
                \begin{eqnarray*}
                    F & = & ( 8 x + 10 ) ( 8 x - 10 ) \\ 
                    F & = & 8 \times 8 x^{  2 } + ( 10 \times 8 + 8 \times ( -10 ) ) x + 10 \times ( -10 ) \\ 
                    F & = & 64 x^{  2 } + ( 80 - 80 ) x - 100 \\ 
                    F & = & 64 x^{  2 } - 100
                \end{eqnarray*}
            \end{solution}


            \part $G = ( 9 x + 7 )^{  2 }$
            \begin{solution}
                \begin{eqnarray*}
                    G & = & ( 9 x + 7 )^{  2 } \\ 
                    G & = & ( 9 x + 7 ) ( 9 x + 7 ) \\ 
                    G & = & 9 \times 9 x^{  2 } + ( 7 \times 9 + 9 \times 7 ) x + 7 \times 7 \\ 
                    G & = & 81 x^{  2 } + ( 63 + 63 ) x + 49 \\ 
                    G & = & 81 x^{  2 } + 126 x + 49
                \end{eqnarray*}
            \end{solution}


            \part $H = ( 4 x - 10 )^{  2 }$
            \begin{solution}
                \begin{eqnarray*}
                    H & = & ( 4 x - 10 )^{  2 } \\ 
                    H & = & ( 4 x - 10 ) ( 4 x - 10 ) \\ 
                    H & = & 4 \times 4 x^{  2 } + ( -10 \times 4 + 4 \times ( -10 ) ) x - 10 \times ( -10 ) \\ 
                    H & = & 16 x^{  2 } + ( -40 - 40 ) x + 100 \\ 
                    H & = & 16 x^{  2 } - 80 x + 100
                \end{eqnarray*}
            \end{solution}

        \end{parts}



\end{questions}

\end{document}

%%% Local Variables: 
%%% mode: latex
%%% TeX-master: "master"
%%% End:
