Feat: ajout le plan de travail sur le calcul littéral

2nd/03_Calcul_litteral/1_exercises.tex

@@ -0,0 +1,162 @@
+\begin{exercise}[subtitle={Réduire - technique}, step={1}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}]
+    Réduire les expressions suivantes
+
+    \begin{multicols}{2}
+        \begin{enumerate}
+            \item $A = 3x - 7 + 10x - 6$
+            \item $B = - 7t - 3 - 10t - 4t$
+            \item $C = 8t - 4 - 3t - 8t$
+            \item $D = - 9x + 2 + 9x - 4$
+            \item $E = 6t - 4 + 4t + 4 + 6t$
+            \item $F = \dfrac{- 3}{3} + 4a - 7a - 2$
+            \item $G = 8x^{2} + 10 + 9x^{2} - 3 - 6x^{2}$
+            \item $H = - 8x + 10 - 4x^{2} - 5 + 4x^{2}$
+            \item $I = 5x - 3 + 3x^{2} - 5x - 7x^{2}$
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+\begin{solution}
+    \begin{multicols}{3}
+        \begin{enumerate}
+            \item
+                \begin{align*}
+                    A & = 3x - 7 + 10x - 6 \\ & = 3x - 7 + 10x - 6 \\ & = 3x + 10x - 7 - 6 \\ & = (3 + 10) \times x - 13 \\ & = 13x - 13
+                \end{align*}
+            \item
+                \begin{align*}
+                    B & = - 7t - 3 - 10t - 4t \\ & = - 7t - 3 + (- 10 - 4) \times t \\ & = - 7t - 3 - 14t \\ & = - 7t - 14t - 3 \\ & = (- 7 - 14) \times t - 3 \\ & = - 21t - 3
+                \end{align*}
+            \item
+                \begin{align*}
+                    C & = 8t - 4 - 3t - 8t \\ & = 8t - 4 + (- 3 - 8) \times t \\ & = 8t - 4 - 11t \\ & = 8t - 11t - 4 \\ & = (8 - 11) \times t - 4 \\ & = - 3t - 4
+                \end{align*}
+            \item
+                \begin{align*}
+                    D & = - 9x + 2 + 9x - 4 \\ & = - 9x + 2 + 9x - 4 \\ & = - 9x + 9x + 2 - 4 \\ & = (- 9 + 9) \times x - 2 \\ & = 0x - 2 \\ & = - 2
+                \end{align*}
+            \item
+                \begin{align*}
+                    E & = 6t - 4 + 4t + 4 + 6t \\ & = 6t - 4 + (4 + 6) \times t + 4 \\ & = 6t - 4 + 4 + 10t \\ & = (6 + 10) \times t + 0 \\ & = 16t
+                \end{align*}
+            \item
+                \begin{align*}
+                    F & = \dfrac{- 3}{3} + 4a - 7a - 2 \\ & = 4a + \dfrac{- 3}{3} - 7a - 2 \\ & = 4a - 7a + \dfrac{- 3}{3} - 2 \\ & = (4 - 7) \times a + \dfrac{- 3}{3} + \dfrac{- 2}{1} \\ & = - 3a + \dfrac{- 3}{3} + \dfrac{- 2 \times 3}{1 \times 3} \\ & = - 3a + \dfrac{- 3}{3} + \dfrac{- 6}{3} \\ & = - 3a + \dfrac{- 3}{3} + \dfrac{- 6}{3} \\ & = - 3a + \dfrac{- 3 - 6}{3} \\ & = - 3a + \dfrac{- 9}{3}
+                \end{align*}
+            \item
+                \begin{align*}
+                    G & = 8x^{2} + 10 + 9x^{2} - 3 - 6x^{2} \\ & = 8x^{2} + 10 + (9 - 6) \times x^{2} - 3 \\ & = 8x^{2} + 10 - 3 + 3x^{2} \\ & = (8 + 3) \times x^{2} + 7 \\ & = 11x^{2} + 7
+                \end{align*}
+            \item
+                \begin{align*}
+                    H & = - 8x + 10 - 4x^{2} - 5 + 4x^{2} \\ & = - 4x^{2} - 8x + 10 - 5 + 4x^{2} \\ & = - 4x^{2} + 4x^{2} - 8x + 10 - 5 \\ & = (- 4 + 4) \times x^{2} - 8x + 5 \\ & = - 8x + 5
+                \end{align*}
+            \item
+                \begin{align*}
+                    I & = 5x - 3 + 3x^{2} - 5x - 7x^{2} \\ & = 3x^{2} + 5x - 3 - 5x - 7x^{2} \\ & = 3x^{2} - 7x^{2} + 5x - 5x - 3 \\ & = (3 - 7) \times x^{2} + (5 - 5) \times x - 3 \\ & = - 4x^{2} - 3
+                \end{align*}
+        \end{enumerate}
+    \end{multicols}
+\end{solution}
+
+\begin{exercise}[subtitle={Développer 1 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}]
+    Réduire les expressions suivantes
+
+    \begin{multicols}{2}
+        \begin{enumerate}
+            \item $A = 10(- 8x + 8)$
+            \item $B = 7(- 4 + 8t)$
+            \item $C = t(3 + 7t)$
+            \item $D = - 9x(7x - 3)$
+            \item $E = 5x(10x - 5)$
+            \item $F = \dfrac{9}{4} \times x(2x + 8)$
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+\begin{solution}
+    \begin{multicols}{3}
+        \begin{enumerate}
+            \item
+                \begin{align*}
+                    A & = 10(- 8x + 8) \\ & = 10 \times - 8x + 10 \times 8 \\ & = 10(- 8) \times x + 80 \\ & = - 80x + 80
+                \end{align*}
+            \item
+                \begin{align*}
+                    B & = 7(- 4 + 8t) \\ & = 7 \times 8t + 7(- 4) \\ & = 7 \times 8 \times t - 28 \\ & = 56t - 28
+                \end{align*}
+            \item
+                \begin{align*}
+                    C & = t(3 + 7t) \\ & = t \times 7t + t \times 3 \\ & = 7t^{2} + 3t
+                \end{align*}
+            \item
+                \begin{align*}
+                    D & = - 9x(7x - 3) \\ & = - 9x \times 7x - 9x(- 3) \\ & = - 9 \times 7 \times x^{1 + 1} - 3(- 9) \times x \\ & = - 63x^{2} + 27x
+                \end{align*}
+            \item
+                \begin{align*}
+                    E & = 5x(10x - 5) \\ & = 5x \times 10x + 5x(- 5) \\ & = 5 \times 10 \times x^{1 + 1} - 5 \times 5 \times x \\ & = 50x^{2} - 25x
+                \end{align*}
+            \item
+                \begin{align*}
+                    F & = \dfrac{9}{4} \times x(2x + 8) \\ & = \dfrac{9}{4} \times x \times 2x + \dfrac{9}{4} \times x \times 8 \\ & = \dfrac{9}{4} \times 2 \times x^{1 + 1} + 8 \times \dfrac{9}{4} \times x \\ & = \dfrac{9 \times 2}{4} \times x^{2} + \dfrac{8 \times 9}{4} \times x \\ & = \dfrac{18}{4} \times x^{2} + \dfrac{72}{4} \times x
+                \end{align*}
+        \end{enumerate}
+    \end{multicols}
+\end{solution}
+
+\begin{exercise}[subtitle={Développer 2 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}]
+    Réduire les expressions suivantes
+
+    \begin{multicols}{2}
+        \begin{enumerate}
+            \item $A = (- 8x - 3)(- 7x - 10)$
+            \item $B = (- 2t + 10)(2t + 6)$
+            \item $C = (- 9x - 5)(3x + 4)$
+            \item $D = (6x - 2)(9x + 10)$
+            \item $E = (- 8x - 4)^{2}$
+            \item $F = (- 8x - 10)^{2}$
+            \item $G = (- 10x + 6)^{2}$
+            \item $H = (\dfrac{- 6}{4} \times x - 7)^{2}$
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+\begin{solution}
+    \begin{multicols}{2}
+        \begin{enumerate}
+            \item
+                \begin{align*}
+                    A & = (- 8x - 3)(- 7x - 10) \\ & = - 8x \times - 7x - 8x(- 10) - 3 \times - 7x - 3(- 10) \\ & = - 8(- 7) \times x^{1 + 1} - 10(- 8) \times x - 3(- 7) \times x + 30 \\ & = 80x + 21x + 56x^{2} + 30 \\ & = (80 + 21) \times x + 56x^{2} + 30 \\ & = 56x^{2} + 101x + 30
+                \end{align*}
+            \item
+                \begin{align*}
+                    B & = (- 2t + 10)(2t + 6) \\ & = - 2t \times 2t - 2t \times 6 + 10 \times 2t + 10 \times 6 \\ & = - 2 \times 2 \times t^{1 + 1} + 6(- 2) \times t + 10 \times 2 \times t + 60 \\ & = - 12t + 20t - 4t^{2} + 60 \\ & = (- 12 + 20) \times t - 4t^{2} + 60 \\ & = - 4t^{2} + 8t + 60
+                \end{align*}
+            \item
+                \begin{align*}
+                    C & = (- 9x - 5)(3x + 4) \\ & = - 9x \times 3x - 9x \times 4 - 5 \times 3x - 5 \times 4 \\ & = - 9 \times 3 \times x^{1 + 1} + 4(- 9) \times x - 5 \times 3 \times x - 20 \\ & = - 36x - 15x - 27x^{2} - 20 \\ & = (- 36 - 15) \times x - 27x^{2} - 20 \\ & = - 27x^{2} - 51x - 20
+                \end{align*}
+            \item
+                \begin{align*}
+                    D & = (6x - 2)(9x + 10) \\ & = 6x \times 9x + 6x \times 10 - 2 \times 9x - 2 \times 10 \\ & = 6 \times 9 \times x^{1 + 1} + 10 \times 6 \times x - 2 \times 9 \times x - 20 \\ & = 60x - 18x + 54x^{2} - 20 \\ & = (60 - 18) \times x + 54x^{2} - 20 \\ & = 54x^{2} + 42x - 20
+                \end{align*}
+            \item
+                \begin{align*}
+                    E & = (- 8x - 4)^{2} \\ & = (- 8x - 4)(- 8x - 4) \\ & = - 8x \times - 8x - 8x(- 4) - 4 \times - 8x - 4(- 4) \\ & = - 8(- 8) \times x^{1 + 1} - 4(- 8) \times x - 4(- 8) \times x + 16 \\ & = 32x + 32x + 64x^{2} + 16 \\ & = (32 + 32) \times x + 64x^{2} + 16 \\ & = 64x^{2} + 64x + 16
+                \end{align*}
+            \item
+                \begin{align*}
+                    F & = (- 8x - 10)^{2} \\ & = (- 8x - 10)(- 8x - 10) \\ & = - 8x \times - 8x - 8x(- 10) - 10 \times - 8x - 10(- 10) \\ & = - 8(- 8) \times x^{1 + 1} - 10(- 8) \times x - 10(- 8) \times x + 100 \\ & = 80x + 80x + 64x^{2} + 100 \\ & = (80 + 80) \times x + 64x^{2} + 100 \\ & = 64x^{2} + 160x + 100
+                \end{align*}
+            \item
+                \begin{align*}
+                    G & = (- 10x + 6)^{2} \\ & = (- 10x + 6)(- 10x + 6) \\ & = - 10x \times - 10x - 10x \times 6 + 6 \times - 10x + 6 \times 6 \\ & = - 10(- 10) \times x^{1 + 1} + 6(- 10) \times x + 6(- 10) \times x + 36 \\ & = - 60x - 60x + 100x^{2} + 36 \\ & = (- 60 - 60) \times x + 100x^{2} + 36 \\ & = 100x^{2} - 120x + 36
+                \end{align*}
+            \item
+                \begin{align*}
+                    H & = (\dfrac{- 6}{4} \times x - 7)^{2} \\ & = (\dfrac{- 6}{4} \times x - 7)(\dfrac{- 6}{4} \times x - 7) \\ & = \dfrac{- 6}{4} \times x \times \dfrac{- 6}{4} \times x + \dfrac{- 6}{4} \times x(- 7) - 7 \times \dfrac{- 6}{4} \times x - 7(- 7) \\ & = \dfrac{- 6}{4} \times \dfrac{- 6}{4} \times x^{1 + 1} - 7 \times \dfrac{- 6}{4} \times x - 7 \times \dfrac{- 6}{4} \times x + 49 \\ & = \dfrac{- 7(- 6)}{4} \times x + \dfrac{- 7(- 6)}{4} \times x + \dfrac{- 6(- 6)}{4 \times 4} \times x^{2} + 49 \\ & = \dfrac{42}{4} \times x + \dfrac{36}{16} \times x^{2} + \dfrac{42}{4} \times x + 49 \\ & = 49 + \dfrac{36}{16} \times x^{2} + \dfrac{42}{4} \times x + \dfrac{42}{4} \times x \\ & = 49 + \dfrac{36}{16} \times x^{2} + (\dfrac{42}{4} + \dfrac{42}{4}) \times x \\ & = 49 + \dfrac{36}{16} \times x^{2} + \dfrac{42 + 42}{4} \times x \\ & = \dfrac{36}{16} \times x^{2} + \dfrac{84}{4} \times x + 49
+                \end{align*}
+        \end{enumerate}
+    \end{multicols}
+\end{solution}

2nd/03_Calcul_litteral/bopytex_config.py

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+# bopytex_config.py
+from mapytex.calculus.random import expression as random_expression
+from mapytex import render
+import random
+
+random.seed(0)  # Controlling the seed allows to make subject reproductible
+
+render.set_render("tex")
+
+direct_access = {
+    "random_expression": random_expression,
+}

2nd/03_Calcul_litteral/exercises.tex

@@ -0,0 +1,101 @@
+\begin{exercise}[subtitle={Programmes de calculs}, step={1}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\searchMode}]
+    Voici 2 programmes de calculs.
+
+    \medskip
+    \setlength\fboxsep{10pt}
+    \Ovalbox{%
+        \begin{minipage}{0.3\linewidth}
+            \textbf{Programme A:} \\
+            Choisir un nombre \\
+            Multiplier par 4 \\
+            Soustraire 1 \\
+            Ajouter le nombre de départ \\
+            Soustraire 2
+        \end{minipage}
+    }
+    \hfill
+    \Ovalbox{%
+        \begin{minipage}{0.3\linewidth}
+            \textbf{Programme B:} \\
+            Choisir un nombre \\
+            Multiplier par 5 \\
+            Enlever 3
+        \end{minipage}
+    }
+
+    \medskip
+
+    Bob pense "\textit{Ces 2 programmes donnent toujours le même résultat.}".
+
+    Qu'en pensez vous?
+\end{exercise}
+
+\begin{exercise}[subtitle={Vrai ou faux}, step={1}, origin={MEpC}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\searchMode}]
+    Pour chacune des affirmations, expliquer si elles sont vraies ou fausses.
+    \begin{enumerate}
+        \item Pour tous les nombres $x$, on a $4+3x = 7x$.
+        \item Pour tous les nombres $y$, on a $y^2 = y$.
+        \item Pour tous les nombres $z$, on a $2z + z - 8 = 3z - 7 - 1$.
+        \item Pour tous les nombres $t$, on a $\dfrac{4t-8}{8} = 4t - 1$.
+        \item Pour lous les nombres $t$, on a $3t + 3 + 5 = t + 2t + 4$.
+    \end{enumerate}
+\end{exercise}
+
+
+\begin{exercise}[subtitle={Aire de rectangles}, step={2}, origin={Classique}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\searchMode}]
+    Trouver deux façons différentes de calculer l'aire de ces rectangles
+    \begin{multicols}{2}
+        \begin{enumerate}
+            \item
+                \begin{tikzpicture}
+                    \draw (0, 0) -- node [midway, below] {1}
+                        (1, 0) coordinate (A) -- node [midway, below] {$x$}
+                        (3, 0) --  node [midway, right] {3}
+                        (3, 2) --
+                        (1, 2)  coordinate (B)--
+                        (0, 2) --
+                        cycle;
+                    \draw (A) -- (B);
+                \end{tikzpicture}
+            \item
+                \begin{tikzpicture}
+                    \draw (0, 0) -- node [midway, below] {$4$}
+                        (3, 0) --   node [midway, right] {$2$}
+                        (3, 1.5) coordinate (A) -- node [midway, right] {$x$}
+                        (3, 2) --
+                        (0, 2) --
+                        (0, 1.5)  coordinate (B)--
+                        cycle;
+                    \draw (A) -- (B);
+                \end{tikzpicture}
+            \item
+                \begin{tikzpicture}
+                    \draw (0, 0) -- node [midway, below] {$x$}
+                        (1, 0) coordinate (A) -- node [midway, below] {$1$}
+                        (3, 0) --  node [midway, right] {$3$}
+                        (3, 1.5) coordinate (C) -- node [midway, right] {$x$}
+                        (3, 2) --
+                        (1, 2)  coordinate (B)--
+                        (0, 2) --
+                        (0, 1.5)  coordinate (D)--
+                        cycle;
+                    \draw (A) -- (B);
+                    \draw (C) -- (D);
+                \end{tikzpicture}
+            \item
+                \begin{tikzpicture}
+                    \draw (0, 0) -- node [midway, below] {$6x$}
+                        (1, 0) coordinate (A) -- node [midway, below] {$3$}
+                        (3, 0) --  node [midway, right] {$2$}
+                        (3, 1.5) coordinate (C) -- node [midway, right] {$2x$}
+                        (3, 2) --
+                        (1, 2)  coordinate (B)--
+                        (0, 2) --
+                        (0, 1.5)  coordinate (D)--
+                        cycle;
+                    \draw (A) -- (B);
+                    \draw (C) -- (D);
+                \end{tikzpicture}
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}

2nd/03_Calcul_litteral/index.rst

@@ -0,0 +1,24 @@
+Calcul littéral
+###############
+
+:date: 2022-09-13
+:modified: 2022-09-13
+:authors: Benjamin Bertrand
+:tags: Calcul littéral
+:category: 2nd
+:summary: Retour sur les bases du calcul littéral
+
+Plan de travail
+===============
+
+Le plan de travail
+
+.. image:: ./plan_de_travail.pdf
+    :height: 200px
+    :alt: Plan de travail
+
+La solution des exercices techniques
+
+.. image:: ./solutions.pdf
+    :height: 200px
+    :alt: Les solutions

2nd/03_Calcul_litteral/plan_de_travail.tex

@@ -0,0 +1,39 @@
+\documentclass[a4paper,12pt]{article}
+\usepackage{myXsim}
+
+\author{Benjamin Bertrand}
+\title{Calcul littéral - Plan de travail}
+\tribe{2nd}
+\date{septembre 2022}
+
+\pagestyle{empty}
+
+\DeclareExerciseCollection{banque}
+\xsimsetup{
+}
+
+\begin{document}
+\maketitle
+
+% Résumé
+
+\bigskip
+
+
+\section{Réduction}
+
+\listsectionexercises
+
+\section{Développement}
+
+\listsectionexercises
+
+
+\pagebreak
+
+\input{exercises.tex}
+\input{1_exercises.tex}
+\printcollection{banque}
+
+
+\end{document}

2nd/03_Calcul_litteral/solutions.tex

@@ -0,0 +1,29 @@
+\documentclass[a4paper,10pt]{article}
+\usepackage{myXsim}
+
+\usetikzlibrary{shapes.geometric}
+
+\author{Benjamin Bertrand}
+\title{Calcul littéral - Solutions}
+\tribe{2nd}
+\date{septembre 2022}
+
+\DeclareExerciseCollection{banque}
+\xsimsetup{
+    exercise/print=false,
+    solution/print=true,
+}
+
+\pagestyle{empty}
+
+
+\begin{document}
+
+\maketitle
+
+\input{exercises.tex}
+\input{1_exercises.tex}
+%\printcollection{banque}
+%\printsolutions{exercises}
+
+\end{document}

2nd/03_Calcul_litteral/tpl_exercises.tex

@@ -0,0 +1,106 @@
+\begin{exercise}[subtitle={Réduire - technique}, step={1}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}]
+    Réduire les expressions suivantes
+    \Block{
+        set reduction = {
+            "A": random_expression("{a}x + {b} + {c}x + {d}", [], global_config={"rejected":[1, 0, -1]}),
+            "B": random_expression("{a}t + {b} + {c}t + {d}t", [], global_config={"rejected":[1, 0, -1]}),
+            "C": random_expression("{a}t + {b} + {c}t + {d}t", [], global_config={"rejected":[1, 0, -1]}),
+            "D": random_expression("{a}x + {b} + {c}x + {d}", ["a+c==0"], global_config={"rejected":[1, 0, -1]}),
+            "E": random_expression("{a}t + {b} + {c}t + {d} + {e}t", ["b+d==0"], global_config={"rejected":[1, 0, -1]}),
+            "F": random_expression("{a}/{k} + {b}a + {c}a + {d}", [], global_config={"rejected":[1, 0, -1]}),
+            "G": random_expression("{a}x^2 + {b} + {c}x^2 + {d} + {e}x^2", [], global_config={"rejected":[1, 0, -1]}),
+            "H": random_expression("{a}x + {b} + {c}x^2 + {d} + {e}x^2", [], global_config={"rejected":[1, 0, -1]}),
+            "I": random_expression("{a}x + {b} + {c}x^2 + {d}x + {e}x^2", ["a+d==0"], global_config={"rejected":[1, 0, -1]}),
+        }
+    }
+    \begin{multicols}{2}
+        \begin{enumerate}
+            %- for (l, e) in reduction.items()
+            \item $\Var{l} = \Var{e}$
+                %- endfor
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+\begin{solution}
+    \begin{multicols}{3}
+        \begin{enumerate}
+            %- for (l, e) in reduction.items()
+            \item
+                \begin{align*}
+                    \Var{l} & = \Var{e.simplify().explain() | join(' \\\\ & = ')}
+                \end{align*}
+                %- endfor
+        \end{enumerate}
+    \end{multicols}
+\end{solution}
+
+\begin{exercise}[subtitle={Développer 1 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}]
+    Réduire les expressions suivantes
+    \Block{
+        set reduction = {
+            "A": random_expression("{a}({c}x + {d})", global_config={"rejected":[1, 0, -1]}),
+            "B": random_expression("{a}({b} + {c}t)", global_config={"rejected":[1, 0, -1]}),
+            "C": random_expression("t({b} + {c}t)", global_config={"rejected":[1, 0, -1]}),
+            "D": random_expression("{a}x({b}x + {c})", global_config={"rejected":[1, 0, -1]}),
+            "E": random_expression("{a}x({b}x + {c})", global_config={"rejected":[1, 0, -1]}),
+            "F": random_expression("{a}/{d}x({b}x + {c})", global_config={"min_max":(1, 10)}),
+        }
+    }
+    \begin{multicols}{2}
+        \begin{enumerate}
+            %- for (l, e) in reduction.items()
+            \item $\Var{l} = \Var{e}$
+                %- endfor
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+\begin{solution}
+    \begin{multicols}{3}
+        \begin{enumerate}
+            %- for (l, e) in reduction.items()
+            \item
+                \begin{align*}
+                    \Var{l} & = \Var{e.simplify().explain() | join(' \\\\ & = ')}
+                \end{align*}
+                %- endfor
+        \end{enumerate}
+    \end{multicols}
+\end{solution}
+
+\begin{exercise}[subtitle={Développer 2 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}]
+    Réduire les expressions suivantes
+    \Block{
+        set reduction = {
+            "A": random_expression("({a}x + {b})({c}x + {d})", global_config={"rejected":[1, 0, -1]}),
+            "B": random_expression("({a}t + {b})({c}t + {d})", global_config={"rejected":[1, 0, -1]}),
+            "C": random_expression("({a}x + {b})({c}x + {d})", global_config={"rejected":[1, 0, -1]}),
+            "D": random_expression("({a}x + {b})({c}x + {d})", global_config={"rejected":[1, 0, -1]}),
+            "E": random_expression("({a}x + {b})^2", global_config={"rejected":[1, 0, -1]}),
+            "F": random_expression("({a}x + {b})^2", global_config={"rejected":[1, 0, -1]}),
+            "G": random_expression("({a}x + {b})^2", global_config={"rejected":[1, 0, -1]}),
+            "H": random_expression("({a}/{c}x + {b})^2", global_config={"rejected":[1, 0, -1]}),
+        }
+    }
+    \begin{multicols}{2}
+        \begin{enumerate}
+            %- for (l, e) in reduction.items()
+            \item $\Var{l} = \Var{e}$
+                %- endfor
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+\begin{solution}
+    \begin{multicols}{2}
+        \begin{enumerate}
+            %- for (l, e) in reduction.items()
+            \item
+                \begin{align*}
+                    \Var{l} & = \Var{e.simplify().explain() | join(' \\\\ & = ')}
+                \end{align*}
+                %- endfor
+        \end{enumerate}
+    \end{multicols}
+\end{solution}