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z-j%0vn^zEh|51q#e^*Wh2NM4DmpQdUv^lvYwGy6iB7cw}tTIG=#1b>=bNLPMxzzZS zck!aZtMAZ$MejrNW%Th}d^R=(O-1~F0cr}}m;e9( diff --git a/2nd/01_Fraction_Developpement_Litteral/4E_reduire.tex b/2nd/01_Fraction_Developpement_Litteral/4E_reduire.tex index 9d603fb..ba6a3d8 100644 --- a/2nd/01_Fraction_Developpement_Litteral/4E_reduire.tex +++ b/2nd/01_Fraction_Developpement_Litteral/4E_reduire.tex @@ -16,5 +16,6 @@ \input{exercises.tex} \printcollection{banque} - +\vfill +\printsolution{exercise}{4} \end{document} diff --git a/2nd/01_Fraction_Developpement_Litteral/exercises.tex b/2nd/01_Fraction_Developpement_Litteral/exercises.tex index b0943ff..ae77c63 100644 --- a/2nd/01_Fraction_Developpement_Litteral/exercises.tex +++ b/2nd/01_Fraction_Developpement_Litteral/exercises.tex @@ -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*} - 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*} + \begin{align*} + B & = & x + 6 + 3 + x - 6 \\ + B & = & 2 x + 3 + \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}