Feat: E6 technique développement et réduction

2nd/01_Fraction_Developpement_Litteral/6E_bilan_dev_red.tex

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+\documentclass[a4paper,10pt]{article}
+\usepackage{myXsim}
+\usepackage{amsmath}
+
+\author{Benjamin Bertrand}
+\title{Information chiffrée 1 - Exercices}
+\date{Octobre 2021}
+
+\pagestyle{empty}
+
+\xsimsetup{
+    solution/print = false
+}
+
+\begin{document}
+
+\begin{exercise}[subtitle={Réductions}]
+    \begin{multicols}{3}
+        \begin{enumerate}[label={\Alph*=}]
+            \item $- 3x - 10 + 4x + 7$
+            \item $3x + 2 - 9x - 7$
+
+            \item $- 9x^{2} - 7 - 7x^{2} + 6 + 6x - 7$
+            \item $- 7x - 1 - 7x + 8 + 4x + 3x$
+
+            \item $3x + 15 + 9x + 18x + 17$
+            \item $- 4x - 5 + 4x + 1$
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+\begin{solution}
+    \begin{multicols}{2}
+        \begin{flalign*}
+            A =& - 3x - 10 + 4x + 7\\ =& - 3x - 10 + 4x + 7\\ =& - 3x + 4x - 10 + 7\\ =& (- 3 + 4) \times x - 3\\ =& x - 3
+        \end{flalign*}
+        \begin{flalign*}
+            B =& 3x + 2 - 9x - 7\\ =& 3x + 2 - 9x - 7\\ =& 3x - 9x + 2 - 7\\ =& (3 - 9) \times x - 5\\ =& - 6x - 5
+        \end{flalign*}
+        \begin{flalign*}
+            C =& - 9x^{2} - 7 - 7x^{2} + 6 + 6x - 7\\ =& - 9x^{2} - 7x^{2} - 7 - 1 + 6x\\ =& (- 9 - 7) \times x^{2} + 6x - 7 - 1\\ =& - 16x^{2} + 6x - 8
+        \end{flalign*}
+        \begin{flalign*}
+            D =& - 7x - 1 - 7x + 8 + 4x + 3x\\ =& - 7x - 1 + 8 - 7x + (4 + 3) \times x\\ =& (- 7 - 7) \times x + 7 + 7x\\ =& - 14x + 7 + 7x\\ =& - 14x + 7x + 7\\ =& (- 14 + 7) \times x + 7\\ =& - 7x + 7
+        \end{flalign*}
+        \begin{flalign*}
+            E =& 3x + 15 + 9x + 18x + 17\\ =& 3x + 15 + (9 + 18) \times x + 17\\ =& 3x + 15 + 17 + 27x\\ =& (3 + 27) \times x + 32\\ =& 30x + 32
+        \end{flalign*}
+        \begin{flalign*}
+            F =& - 4x - 5 + 4x + 1\\ =& - 4x - 5 + 4x + 1\\ =& - 4x + 4x - 5 + 1\\ =& (- 4 + 4) \times x - 4\\ =& 0x - 4\\ =& - 4
+        \end{flalign*}
+    \end{multicols}
+\end{solution}
+
+\begin{exercise}[subtitle={Simple développement}]
+    \begin{multicols}{3}
+        \begin{enumerate}[label={\Alph*=}]
+            \item $10(x + 3)$
+            \item $8(- 10x + 2)$
+            \item $3(- 9x + 3)$
+
+            \item $- 10x(- 6x + 3)$
+            \item $2x(10x - 2) - 4$
+            \item $- 3x - 7x(- 10x + 9)$
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+\begin{solution}
+    \begin{multicols}{2}
+        \begin{flalign*}
+            A =& 10(x + 3)\\ =& 10x + 10 \times 3\\ =& 10x + 30
+        \end{flalign*}
+        \begin{flalign*}
+            B =& 8(- 10x + 2)\\ =& 8 \times - 10x + 8 \times 2\\ =& 8(- 10) \times x + 16\\ =& - 80x + 16
+        \end{flalign*}
+        \begin{flalign*}
+            C =& 3(- 9x + 3)\\ =& 3 \times - 9x + 3 \times 3\\ =& 3(- 9) \times x + 9\\ =& - 27x + 9
+        \end{flalign*}
+        \begin{flalign*}
+            D =& - 10x(- 6x + 3)\\ =& - 10x \times - 6x - 10x \times 3\\ =& - 10(- 6) \times x^{1 + 1} + 3(- 10) \times x\\ =& 60x^{2} - 30x
+        \end{flalign*}
+        \begin{flalign*}
+            E =& 2x(10x - 2) - 4\\ =& 2x \times 10x + 2x(- 2) - 4\\ =& 2 \times 10 \times x^{1 + 1} - 2 \times 2 \times x - 4\\ =& 20x^{2} - 4x - 4
+        \end{flalign*}
+        \begin{flalign*}
+            F =& - 3x - 7x(- 10x + 9)\\ =& - 3x - 7x \times - 10x - 7x \times 9\\ =& - 3x - 7(- 10) \times x^{1 + 1} + 9(- 7) \times x\\ =& - 3x - 63x + 70x^{2}\\ =& (- 3 - 63) \times x + 70x^{2}\\ =& 70x^{2} - 66x
+        \end{flalign*}
+    \end{multicols}
+\end{solution}
+
+\begin{exercise}[subtitle={Double développement}]
+    \begin{multicols}{3}
+        \begin{enumerate}[label={\Alph*=}]
+            \item $(x + 10)(x + 6)$
+            \item $(8x - 6)(- 5x - 10)$
+            \item $(- 6x + 9)(7x - 3)$
+
+            \item $(5x + 2)(- 6x + 2)$
+            \item $(- 8x + 8)^{2}$
+            \item $(2x - 6)^{2}$
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+\begin{solution}
+    \begin{multicols}{2}
+        \begin{flalign*}
+            A =& 10(x + 3)\\ =& 10x + 10 \times 3\\ =& 10x + 30
+        \end{flalign*}
+        \begin{flalign*}
+            B =& 8(- 10x + 2)\\ =& 8 \times - 10x + 8 \times 2\\ =& 8(- 10) \times x + 16\\ =& - 80x + 16
+        \end{flalign*}
+        \begin{flalign*}
+            C =& 3(- 9x + 3)\\ =& 3 \times - 9x + 3 \times 3\\ =& 3(- 9) \times x + 9\\ =& - 27x + 9
+        \end{flalign*}
+        \begin{flalign*}
+            D =& - 10x(- 6x + 3)\\ =& - 10x \times - 6x - 10x \times 3\\ =& - 10(- 6) \times x^{1 + 1} + 3(- 10) \times x\\ =& 60x^{2} - 30x
+        \end{flalign*}
+        \begin{flalign*}
+            E =& 2x(10x - 2) - 4\\ =& 2x \times 10x + 2x(- 2) - 4\\ =& 2 \times 10 \times x^{1 + 1} - 2 \times 2 \times x - 4\\ =& 20x^{2} - 4x - 4
+        \end{flalign*}
+        \begin{flalign*}
+            F =& - 3x - 7x(- 10x + 9)\\ =& - 3x - 7x \times - 10x - 7x \times 9\\ =& - 3x - 7(- 10) \times x^{1 + 1} + 9(- 7) \times x\\ =& - 3x - 63x + 70x^{2}\\ =& (- 3 - 63) \times x + 70x^{2}\\ =& 70x^{2} - 66x
+        \end{flalign*}
+    \end{multicols}
+\end{solution}
+
+\vfill
+
+\printexercise{exercise}{1}
+\printexercise{exercise}{2}
+\printexercise{exercise}{3}
+\vfill
+
+\printexercise{exercise}{1}
+\printexercise{exercise}{2}
+\printexercise{exercise}{3}
+
+\newpage
+
+\printsolutionstype{exercise}
+
+\end{document}

2nd/01_Fraction_Developpement_Litteral/tpl_6E_bilan_dev_red.tex

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+\documentclass[a4paper,10pt]{article}
+\usepackage{myXsim}
+\usepackage{amsmath}
+
+\author{Benjamin Bertrand}
+\title{Information chiffrée 1 - Exercices}
+\date{Octobre 2021}
+
+\xsimsetup{
+    solution/print = false
+}
+
+\begin{document}
+
+\begin{exercise}[subtitle={Réductions}]
+    Développer puis réduire les expressions suivantes
+    \begin{multicols}{3}
+        \begin{enumerate}[label={\Alph*=}]
+            %- set a = Expression.random("{a}x + {b} + {c}x + {d}")
+            \item $\Var{a}$
+            %- set b = Expression.random("{a}x + {b} + {c}x + {d}")
+            \item $\Var{b}$
+
+            %- set c = Expression.random("{a}x^2 + {b} + {c}x^2 + {d} + {d}x + {e}")
+            \item $\Var{c}$
+            %- set d = Expression.random("{a}x + {b} + {c}x + {d} + {e}x + {f}x")
+            \item $\Var{d}$
+
+                %- set e = Expression.random("{a}*x + {b} + {c}x + {d}x + {e}", min_max=(2, 20))
+            \item $\Var{e}$
+            %- set f = Expression.random("{a}x + {b} + {c}x + {d}", conditions=["a+c==0"])
+            \item $\Var{f}$
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+\begin{solution}
+    \begin{multicols}{2}
+        \begin{flalign*}
+            A =& \Var{a.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+        \begin{flalign*}
+            B =& \Var{b.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+        \begin{flalign*}
+            C =& \Var{c.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+        \begin{flalign*}
+            D =& \Var{d.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+        \begin{flalign*}
+            E =& \Var{e.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+        \begin{flalign*}
+            F =& \Var{f.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+    \end{multicols}
+\end{solution}
+
+\begin{exercise}[subtitle={Simple développement}]
+    Développer puis réduire les expressions suivantes
+    \begin{multicols}{3}
+        \begin{enumerate}[label={\Alph*=}]
+            %- set a = Expression.random("{a}*(x + {b})", rejected=[-1,0,1])
+            \item $\Var{a}$
+                %- set b = Expression.random("{a}*({c}x + {d})", rejected=[-1,0,1])
+            \item $\Var{b}$
+                %- set c = Expression.random("{a}*({c}x + {d})", rejected=[-1,0,1])
+            \item $\Var{c}$
+
+                %- set d = Expression.random("{c}*x*({a}x + {b})", rejected=[-1,0,1])
+            \item $\Var{d}$
+                %- set e = Expression.random("{a}*x*({b}x + {c}) + {d}", rejected=[-1,0,1])
+            \item $\Var{e}$
+                %- set f = Expression.random("{c}*x + {d}*x*({a}x + {b})", rejected=[-1,0,1])
+            \item $\Var{f}$
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+\begin{solution}
+    \begin{multicols}{2}
+        \begin{flalign*}
+            A =& \Var{a.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+        \begin{flalign*}
+            B =& \Var{b.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+        \begin{flalign*}
+            C =& \Var{c.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+        \begin{flalign*}
+            D =& \Var{d.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+        \begin{flalign*}
+            E =& \Var{e.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+        \begin{flalign*}
+            F =& \Var{f.simplify().explain() | join('\\\ =& ')}
+        \end{flalign*}
+    \end{multicols}
+\end{solution}
+
+\begin{exercise}[subtitle={Double développement}]
+    Développer puis réduire les expressions suivantes
+    \begin{multicols}{3}
+        \begin{enumerate}[label={\Alph*=}]
+            %- set a = Expression.random("(x + {a})*(x + {b})", rejected=[-1,0,1])
+            \item $\Var{a}$
+                %- set b = Expression.random("({a}x + {b})*({c}x + {d})", rejected=[-1,0,1])
+            \item $\Var{b}$
+                %- set c = Expression.random("({a}x + {b})*({c}x + {d})", rejected=[-1,0,1])
+            \item $\Var{c}$
+
+                %- set d = Expression.random("({c}*x + {d})*({a}x + {b})", rejected=[-1,0,1])
+            \item $\Var{d}$
+                %- set e = Expression.random("({b}x + {c})^2", rejected=[-1,0,1])
+            \item $\Var{e}$
+                %- set f = Expression.random("({a}x + {b})^2", rejected=[-1,0,1])
+            \item $\Var{f}$
+        \end{enumerate}
+    \end{multicols}
+\end{exercise}
+
+
+\newpage
+
+\printsolutionstype{exercise}
+
+\end{document}