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% Title Page
\titre{Technique: Evaluer et reduire}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Troisième}
\date{Novembre 2016}
%\duree{1 heure}
\sujet{\Var{infos.num}}
% DS DSCorr DM DMCorr Corr

%\printanswers
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\newcommand{\lesexos}{%
    \begin{Exo}
    Évaluer les expressions suivantes

    \begin{multicols}{3}
        \begin{enumerate}
            \Block{set P = Polynom.random(degree = 1)}
            \Block{set x = Expression.random("{a}")}
        \item $\Var{P}$ en $x = \Var{x}$
            \begin{solution}
                \begin{eqnarray*}
                    \Var{P(x).explain()| calculus()}
                \end{eqnarray*}
            \end{solution}
            \Block{set P = Polynom.random(degree = 1)}
            \Block{set x = Expression.random("{a}")}
        \item $\Var{P}$ en $x = \Var{x}$
            \begin{solution}
                \begin{eqnarray*}
                    \Var{P(x).explain()| calculus()}
                \end{eqnarray*}
            \end{solution}
            \Block{set x = Expression.random("{a}")}
        \item $\Var{P}$ en $x = \Var{x}$
            \begin{solution}
                \begin{eqnarray*}
                    \Var{P(x).explain()| calculus()}
                \end{eqnarray*}
            \end{solution}

            \Block{set P = Polynom.random(degree = 2)}
            \Block{set x = Expression.random("{a}")}
        \item $\Var{P}$ en $x = \Var{x}$
            \begin{solution}
                \begin{eqnarray*}
                    \Var{P(x).explain()| calculus()}
                \end{eqnarray*}
            \end{solution}
            \Block{set x = Expression.random("{a}")}
        \item $\Var{P}$ en $x = \Var{x}$
            \begin{solution}
                \begin{eqnarray*}
                    \Var{P(x).explain()| calculus()}
                \end{eqnarray*}
            \end{solution}
        \Block{set P = Polynom.random(degree = 2)}
        \Block{set x = Expression.random("{a}")}
        \item $\Var{P}$ en $x = \Var{x}$
            \begin{solution}
                \begin{eqnarray*}
                    \Var{P(x).explain()| calculus()}
                \end{eqnarray*}
            \end{solution}
            \Block{set P = Expression.random("{a} x * (x - {b})")}
        \Block{set x = Expression.random("{a}")}
        \item $\Var{P}$ en $x = \Var{x}$
            \Block{set x = Expression.random("{a}")}
        \item $\Var{P}$ en $x = \Var{x}$
            \Block{set P = Expression.random("({a}x + {b})({c} + {d}x)")}
            \Block{set x = Expression.random("{a}")}
        \item $\Var{P}$ en $x = \Var{x}$
        \end{enumerate}
    \end{multicols}
    \end{Exo}

    \begin{Exo}
        Réduis les expressions suivantes

        \begin{multicols}{3}
            \begin{enumerate}
                \Block{set A = Expression.random("x + {a} + x - {b}")}
                \item A = $\Var{A}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{A.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}
                    \Block{set B = Expression.random("x + {a} + {c} + x - {b}")}
                \item B = $\Var{B}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{B.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}
                    \Block{set C = Expression.random("{a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
                \item C = $\Var{C}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{C.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}

                    \Block{set D = Expression.random("{b} + {a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
                \item D = $\Var{D}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{D.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}
                    \Block{set E = Expression.random("({b} - {a}) + {a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
                \item E = $\Var{E}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{E.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}
                    \Block{set E = Expression.random("x^2 + {c} + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
                \item E = $\Var{E}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{E.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}

                    \Block{set F = Expression.random("{a}x^2 + {c} + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
                \item F = $\Var{F}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{F.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}
                    \Block{set G = Expression.random("{a}x^2 + {c}x^2 + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
                \item G = $\Var{G}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{G.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}
                    \Block{set G = Expression.random("{a}x^2 + {c}+ {d}x + {d}x^2 + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
                \item G = $\Var{G}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{G.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}
            \end{enumerate}
        \end{multicols}
    \end{Exo}
}

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