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% Title Page
\titre{1}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Troisième}
\date{Mercredi 9 décembre 2015}
%\duree{1 heure}
\sujet{\Var{infos.num}}
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\typedoc{DM}

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\begin{document}

\begin{questions}

    \question
    Reduire les expressions suivantes.
    \begin{multicols}{2}
    \begin{parts}
        \Block{set e = Expression.random("{a}x + {b}x + {c} + {d}x", val_min= 2)}
        \part $A = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "A")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a} + {b}x + {c} + {d}x + {e}", val_min= 2)}
        \part $B = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "B")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a}x + {b}x + {c} + {d}x")}
        \part $C = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "C")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a} + {b}x + {c} + {d}x + {e}")}
        \part $D = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "D")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a}x*{e} + {b} + {c}", val_min= 2)}
        \part $E = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "E")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a}x*{b}x + {c} + {d}x + {e}", val_min= 2)}
        \part $F = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "F")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a}x*{e} + {b}*{e} + {c}")}
        \part $G = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "G")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a}x*{b}x + {c} + {d}x + {e}*{e}", val_min= 2)}
        \part $H = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "H")}
            \end{eqnarray*}
        \end{solution}
    \end{parts}
    \end{multicols}

    \question
    Developper et reduire les expressions suivantes.
    \begin{multicols}{2}
    \begin{parts}
        \Block{set e = Expression.random("{a}({b}x + {c})")}
        \part $A = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "A")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a}({b}x + {c})")}
        \part $B = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "B")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a}x({b}x + {c})")}
        \part $C = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "C")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a}x({b}x + {c})")}
        \part $D = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "D")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a}({b}x + {c}) + {e}")}
        \part $E = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "E")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("{a}x({b}x + {c}) + {e}")}
        \part $F = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "F")}
            \end{eqnarray*}
        \end{solution}
    \end{parts}
    \end{multicols}

    \question
    Developper et reduire les expressions suivantes.
    \begin{multicols}{2}
    \begin{parts}
        \Block{set e = Expression.random("({a}x + {d})({b}x + {c})")}
        \part $A = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "A")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x + {d})({b}x + {c})")}
        \part $B = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "B")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x + {d})({b}x + {c})")}
        \part $C = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "C")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x + {d})({b}x + {c})")}
        \part $D = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "D")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x + {d})({b}x + {c})")}
        \part $E = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "E")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x + {d})({b}x + {c})")}
        \part $F = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "F")}
            \end{eqnarray*}
        \end{solution}
    \end{parts}
    \end{multicols}

    \question
    Developper et reduire les expressions suivantes.
    \begin{multicols}{2}
    \begin{parts}
        \Block{set e = Expression.random("({a}x + {d})^2", val_min = 2)}
        \part $A = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "A")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x + {d})^2", val_min = 2)}
        \part $B = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "B")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x - {d})^2", val_min = 2)}
        \part $C = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "C")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x - {d})^2", val_min = 2)}
        \part $D = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "D")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x + {d})({a}x - {d})", val_min = 2)}
        \part $E = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "E")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x + {d})({a}x - {d})", val_min = 2)}
        \part $F = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "F")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x + {d})^2", val_min = 2)}
        \part $G = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "G")}
            \end{eqnarray*}
        \end{solution}

        \Block{set e = Expression.random("({a}x - {d})^2", val_min = 2)}
        \part $H = \Var{e}$
        \begin{solution}
            \begin{eqnarray*}
                \Var{e.simplify().explain() | calculus(name = "H")}
            \end{eqnarray*}
        \end{solution}

    \end{parts}
    \end{multicols}



\end{questions}

\end{document}

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