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Feat: réduire pour les 2nd

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Bertrand Benjamin 2021-10-05 09:23:56 +02:00
parent 36e171896f
commit e19bc45905
3 changed files with 50 additions and 103 deletions
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2nd/01_Fraction_Developpement_Litteral/4E_reduire.pdf
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2nd/01_Fraction_Developpement_Litteral/4E_reduire.tex
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@ -16,5 +16,6 @@
\input{exercises.tex}
\printcollection{banque}
\vfill
\printsolution{exercise}{4}
\end{document}

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2nd/01_Fraction_Developpement_Litteral/exercises.tex
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@ -86,122 +86,68 @@
\begin{enumerate}
\item A = $x + 1 + x - 4$
\begin{solution}
\end{solution}
\item B = $x + 6 + 3 + x - 6$
\begin{solution}
\end{solution}
\item C = $-3 x + 5 + 5 x$
\begin{solution}
\begin{eqnarray*}
A & = & -3 x + 5 + 5 x \\
A & = & -3 x + 5 x + 5 \\
A & = & ( -3 + 5 ) x + 5 \\
A & = & 2 x + 5
\end{eqnarray*}
\end{solution}
\item D = $-4 + 2 x - 10 - 10 x$
\begin{solution}
\begin{eqnarray*}
A & = & -4 + 2 x - 10 - 10 x \\
A & = & 2 x - 4 - 10 - 10 x \\
A & = & 2 x - 14 - 10 x \\
A & = & 2 x - 10 x - 14 \\
A & = & ( 2 - 10 ) x - 14 \\
A & = & -8 x - 14
\end{eqnarray*}
\end{solution}
\item E = $-1 - 8 + 8 x + 6 - 4 x$
\begin{solution}
\begin{eqnarray*}
A & = & -1 - 8 + 8 x + 6 - 4 x \\
A & = & -9 + 8 x + 6 - 4 x \\
A & = & 8 x - 9 + 6 - 4 x \\
A & = & 8 x - 3 - 4 x \\
A & = & 8 x - 4 x - 3 \\
A & = & ( 8 - 4 ) x - 3 \\
A & = & 4 x - 3
\end{eqnarray*}
\end{solution}
\item E = $x^{ 2 } + 3 + 3 x + 3 - 10 x$
\begin{solution}
\begin{eqnarray*}
A & = & x^{ 2 } + 3 + 3 x + 3 - 10 x \\
A & = & x^{ 2 } + 3 x + 3 + 3 - 10 x \\
A & = & x^{ 2 } + 3 x + 6 - 10 x \\
A & = & x^{ 2 } + 3 x - 10 x + 6 \\
A & = & x^{ 2 } + ( 3 - 10 ) x + 6 \\
A & = & x^{ 2 } - 7 x + 6
\end{eqnarray*}
\end{solution}
\item F = $-6 x^{ 2 } + 9 - 2 x - 2 - 6 x$
\begin{solution}
\begin{eqnarray*}
A & = & -6 x^{ 2 } + 9 - 2 x - 2 - 6 x \\
A & = & -6 x^{ 2 } - 2 x + 9 - 2 - 6 x \\
A & = & -6 x^{ 2 } - 2 x + 7 - 6 x \\
A & = & -6 x^{ 2 } - 2 x - 6 x + 7 \\
A & = & -6 x^{ 2 } + ( -2 - 6 ) x + 7 \\
A & = & -6 x^{ 2 } - 8 x + 7
\end{eqnarray*}
\end{solution}
\item G = $3 x^{ 2 } + 1 x^{ 2 } - 9 x - 9 + 3 x$
\begin{solution}
\begin{eqnarray*}
A & = & 3 x^{ 2 } + 1 x^{ 2 } - 9 x - 9 + 3 x \\
A & = & 3 x^{ 2 } + x^{ 2 } - 9 x - 9 + 3 x \\
A & = & ( 3 + 1 ) x^{ 2 } - 9 x - 9 + 3 x \\
A & = & 4 x^{ 2 } - 9 x - 9 + 3 x \\
A & = & 4 x^{ 2 } - 9 x + 3 x - 9 \\
A & = & 4 x^{ 2 } + ( -9 + 3 ) x - 9 \\
A & = & 4 x^{ 2 } - 6 x - 9
\end{eqnarray*}
\end{solution}
\item G = $-2 x^{ 2 } + 7 - 6 x - 6 x^{ 2 } - 2 x$
\begin{solution}
\begin{eqnarray*}
A & = & -2 x^{ 2 } + 7 - 6 x - 6 x^{ 2 } - 2 x \\
A & = & -2 x^{ 2 } - 6 x + 7 - 6 x^{ 2 } - 2 x \\
A & = & -2 x^{ 2 } - 6 x^{ 2 } - 6 x + 7 - 2 x \\
A & = & ( -2 - 6 ) x^{ 2 } - 6 x + 7 - 2 x \\
A & = & -8 x^{ 2 } - 6 x + 7 - 2 x \\
A & = & -8 x^{ 2 } - 6 x - 2 x + 7 \\
A & = & -8 x^{ 2 } + ( -6 - 2 ) x + 7 \\
A & = & -8 x^{ 2 } - 8 x + 7
\end{eqnarray*}
\end{solution}
\item F = $x^{ 2 } + 3 + 3 x + 3 - 10 x$
\item G = $-6 x^{ 2 } + 9 - 2 x - 2 - 6 x$
\item H = $3 x^{ 2 } + 1 x^{ 2 } - 9 x - 9 + 3 x$
\item I = $-2 x^{ 2 } + 7 - 6 x - 6 x^{ 2 } - 2 x$
\end{enumerate}
\end{multicols}
\end{exercise}
\begin{solution}
\begin{multicols}{3}
\begin{enumerate}
\item
\begin{eqnarray*}
\begin{align*}
A & = & x + 1 + x - 4 \\
A & = & x + x + 1 - 4 \\
A & = & ( 1 + 1 ) x + 1 - 4 \\
A & = & 2 x - 3
\end{eqnarray*}
\end{align*}
\item
\begin{eqnarray*}
\begin{align*}
B & = & x + 6 + 3 + x - 6 \\
B & = & x + 9 + x - 6 \\
B & = & x + x + 9 - 6 \\
B & = & ( 1 + 1 ) x + 9 - 6 \\
B & = & 2 x + 3
\end{eqnarray*}
\end{align*}
\item
\begin{align*}
C & = & -3 x + 5 + 5 x \\
C & = & 2 x + 5
\end{align*}
\item
\begin{align*}
D & = & -4 + 2 x - 10 - 10 x \\
D & = & -8 x - 14
\end{align*}
\item
\begin{align*}
E & = & -1 - 8 + 8 x + 6 - 4 x \\
E & = & -9 + 8 x + 6 - 4 x \\
E & = & 4 x - 3
\end{align*}
\item
\begin{align*}
F & = & x^{ 2 } + 3 + 3 x + 3 - 10 x \\
F & = & x^{ 2 } - 7 x + 6
\end{align*}
\item
\begin{align*}
G & = & -6 x^{ 2 } + 9 - 2 x - 2 - 6 x \\
G & = & -6 x^{ 2 } - 8 x + 7
\end{align*}
\item
\begin{align*}
H & = & 3 x^{ 2 } + 1 x^{ 2 } - 9 x - 9 + 3 x \\
H & = & 4 x^{ 2 } - 6 x - 9
\end{align*}
\item
\begin{align*}
I & = & -2 x^{ 2 } + 7 - 6 x - 6 x^{ 2 } - 2 x \\
I & = & -8 x^{ 2 } - 8 x + 7
\end{align*}
\end{enumerate}
\end{multicols}
\end{solution}