375 lines
13 KiB
TeX
375 lines
13 KiB
TeX
\documentclass[a5paper,10pt, table]{/media/documents/Cours/Prof/Enseignements/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
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%\geometry{left=10mm,right=10mm, top=10mm, bottom=10mm}
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% Title Page
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\titre{Developper et reduire}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Troisième}
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\date{Janvier 2016}
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%\duree{1 heure}
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\sujet{1}
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% DS DSCorr DM DMCorr Corr
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\typedoc{DM}
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\geometry{left=10mm,right=10mm, bottom= 10mm, top=10mm}
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\printanswers
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\pagestyle{empty}
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\begin{document}
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\begin{questions}
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\question
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Reduire les expressions suivantes.
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\begin{parts}
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\part $A = 3 x + 6 x + 8 + 5 x$
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\begin{solution}
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\begin{eqnarray*}
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A & = & 3 x + 6 x + 8 + 5 x \\
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A & = & ( 3 + 6 ) x + 8 + 5 x \\
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A & = & 9 x + 8 + 5 x \\
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A & = & ( 9 + 5 ) x + 8 \\
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A & = & 14 x + 8
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\end{eqnarray*}
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\end{solution}
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\part $B = 5 + 9 x + 2 + 7 x + 9$
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\begin{solution}
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\begin{eqnarray*}
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B & = & 5 + 9 x + 2 + 7 x + 9 \\
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B & = & 9 x + 5 + 2 + 7 x + 9 \\
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B & = & 9 x + 7 + 7 x + 9 \\
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B & = & ( 9 + 7 ) x + 7 + 9 \\
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B & = & 16 x + 7 + 9 \\
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B & = & 16 x + 16
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\end{eqnarray*}
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\end{solution}
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\part $C = 1 x + 7 x - 6 + 3 x$
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\begin{solution}
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\begin{eqnarray*}
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C & = & 1 x + 7 x - 6 + 3 x \\
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C & = & x + 7 x - 6 + 3 x \\
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C & = & ( 1 + 7 ) x - 6 + 3 x \\
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C & = & 8 x - 6 + 3 x \\
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C & = & ( 8 + 3 ) x - 6 \\
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C & = & 11 x - 6
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\end{eqnarray*}
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\end{solution}
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\part $D = -4 + 9 x - 9 - 8 x - 2$
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\begin{solution}
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\begin{eqnarray*}
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D & = & -4 + 9 x - 9 - 8 x - 2 \\
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D & = & 9 x - 4 - 9 - 8 x - 2 \\
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D & = & 9 x - 13 - 8 x - 2 \\
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D & = & ( 9 - 8 ) x - 13 - 2 \\
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D & = & x - 13 - 2 \\
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D & = & x - 15
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\end{eqnarray*}
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\end{solution}
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\part $E = 9 x \times 5 + 8 + 10$
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\begin{solution}
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\begin{eqnarray*}
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E & = & 9 x \times 5 + 8 + 10 \\
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E & = & 9 \times 5 x + 8 + 10 \\
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E & = & 45 x + 8 + 10 \\
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E & = & 45 x + 18
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\end{eqnarray*}
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\end{solution}
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\part $F = 9 x \times 6 x + 3 + 6 x + 8$
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\begin{solution}
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\begin{eqnarray*}
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F & = & 9 x \times 6 x + 3 + 6 x + 8 \\
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F & = & 9 \times 6 x x + 3 + 6 x + 8 \\
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F & = & 54 x x + 3 + 6 x + 8 \\
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F & = & 54 x^{ 2 } + 3 + 6 x + 8 \\
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F & = & 54 x^{ 2 } + 6 x + 3 + 8 \\
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F & = & 54 x^{ 2 } + 6 x + 11
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\end{eqnarray*}
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\end{solution}
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\part $G = -8 x \times ( -2 ) - 4 \times ( -2 ) - 4$
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\begin{solution}
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\begin{eqnarray*}
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G & = & -8 x \times ( -2 ) - 4 \times ( -2 ) - 4 \\
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G & = & - 8 x \times ( -2 ) + 8 - 4 \\
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G & = & -8 \times ( -2 ) x + 8 - 4 \\
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G & = & 16 x + 8 - 4 \\
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G & = & 16 x + 4
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\end{eqnarray*}
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\end{solution}
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\part $H = 7 x \times 2 x + 10 + 7 x + 3 \times 3$
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\begin{solution}
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\begin{eqnarray*}
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H & = & 7 x \times 2 x + 10 + 7 x + 3 \times 3 \\
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H & = & 7 x \times 2 x + 10 + 7 x + 9 \\
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H & = & 7 \times 2 x x + 10 + 7 x + 9 \\
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H & = & 14 x x + 10 + 7 x + 9 \\
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H & = & 14 x^{ 2 } + 10 + 7 x + 9 \\
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H & = & 14 x^{ 2 } + 7 x + 10 + 9 \\
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H & = & 14 x^{ 2 } + 7 x + 19
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\end{eqnarray*}
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\end{solution}
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\end{parts}
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\question
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Developper et reduire les expressions suivantes.
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\begin{parts}
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\part $A = 5 ( 8 x + 7 )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & 5 ( 8 x + 7 ) \\
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A & = & 5 \times 8 x + 5 \times 7 \\
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A & = & 40 x + 35
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\end{eqnarray*}
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\end{solution}
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\part $B = 9 ( -6 x + 9 )$
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\begin{solution}
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\begin{eqnarray*}
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B & = & 9 ( -6 x + 9 ) \\
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B & = & 9 \times ( -6 ) x + 9 \times 9 \\
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B & = & - 54 x + 81
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\end{eqnarray*}
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\end{solution}
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\part $C = 4 x ( 2 x - 7 )$
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\begin{solution}
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\begin{eqnarray*}
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C & = & 4 x ( 2 x - 7 ) \\
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C & = & 4 \times 2 x^{ 2 } + 4 \times ( -7 ) x \\
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C & = & 8 x^{ 2 } - 28 x
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\end{eqnarray*}
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\end{solution}
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\part $D = 4 x ( -2 x + 9 )$
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\begin{solution}
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\begin{eqnarray*}
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D & = & 4 x ( -2 x + 9 ) \\
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D & = & 4 \times ( -2 ) x^{ 2 } + 4 \times 9 x \\
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D & = & - 8 x^{ 2 } + 36 x
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\end{eqnarray*}
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\end{solution}
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\part $E = -7 ( -9 x + 6 ) + 2$
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\begin{solution}
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\begin{eqnarray*}
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E & = & -7 ( -9 x + 6 ) + 2 \\
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E & = & -7 \times ( -9 ) x - 7 \times 6 + 2 \\
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E & = & 63 x - 42 + 2 \\
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E & = & 63 x - 40
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\end{eqnarray*}
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\end{solution}
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\part $F = -4 x ( -1 x + 3 ) + 3$
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\begin{solution}
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\begin{eqnarray*}
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F & = & -4 x ( -1 x + 3 ) + 3 \\
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F & = & - 4 x ( - x + 3 ) + 3 \\
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F & = & -4 \times ( -1 ) x^{ 2 } - 4 \times 3 x + 3 \\
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F & = & 4 x^{ 2 } - 12 x + 3
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\end{eqnarray*}
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\end{solution}
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\end{parts}
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\question
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Developper et reduire les expressions suivantes.
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\begin{parts}
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\part $A = ( 1 x - 9 ) ( 1 x + 7 )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( 1 x - 9 ) ( 1 x + 7 ) \\
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A & = & ( x - 9 ) ( x + 7 ) \\
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A & = & x^{ 2 } + ( -9 + 7 ) x - 9 \times 7 \\
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A & = & x^{ 2 } - 2 x - 63
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\end{eqnarray*}
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\end{solution}
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\part $B = ( 4 x + 5 ) ( 10 x - 2 )$
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\begin{solution}
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\begin{eqnarray*}
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B & = & ( 4 x + 5 ) ( 10 x - 2 ) \\
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B & = & 4 \times 10 x^{ 2 } + ( 5 \times 10 + 4 \times ( -2 ) ) x + 5 \times ( -2 ) \\
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B & = & 40 x^{ 2 } + ( 50 - 8 ) x - 10 \\
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B & = & 40 x^{ 2 } + 42 x - 10
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\end{eqnarray*}
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\end{solution}
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\part $C = ( -6 x - 9 ) ( -10 x - 7 )$
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\begin{solution}
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\begin{eqnarray*}
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C & = & ( -6 x - 9 ) ( -10 x - 7 ) \\
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C & = & -6 \times ( -10 ) x^{ 2 } + ( -9 \times ( -10 ) - 6 \times ( -7 ) ) x - 9 \times ( -7 ) \\
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C & = & 60 x^{ 2 } + ( 90 + 42 ) x + 63 \\
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C & = & 60 x^{ 2 } + 132 x + 63
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\end{eqnarray*}
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\end{solution}
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\part $D = ( -5 x + 2 ) ( -8 x + 6 )$
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\begin{solution}
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\begin{eqnarray*}
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D & = & ( -5 x + 2 ) ( -8 x + 6 ) \\
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D & = & -5 \times ( -8 ) x^{ 2 } + ( 2 \times ( -8 ) - 5 \times 6 ) x + 2 \times 6 \\
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D & = & 40 x^{ 2 } + ( -16 - 30 ) x + 12 \\
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D & = & 40 x^{ 2 } - 46 x + 12
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\end{eqnarray*}
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\end{solution}
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\part $E = ( -6 x + 2 ) ( 2 x + 5 )$
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\begin{solution}
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\begin{eqnarray*}
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E & = & ( -6 x + 2 ) ( 2 x + 5 ) \\
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E & = & -6 \times 2 x^{ 2 } + ( 2 \times 2 - 6 \times 5 ) x + 2 \times 5 \\
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E & = & - 12 x^{ 2 } + ( 4 - 30 ) x + 10 \\
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E & = & - 12 x^{ 2 } - 26 x + 10
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\end{eqnarray*}
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\end{solution}
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\part $F = ( 1 x - 4 ) ( 9 x + 10 )$
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\begin{solution}
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\begin{eqnarray*}
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F & = & ( 1 x - 4 ) ( 9 x + 10 ) \\
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F & = & ( x - 4 ) ( 9 x + 10 ) \\
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F & = & 9 x^{ 2 } + ( -4 \times 9 + 10 ) x - 4 \times 10 \\
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F & = & 9 x^{ 2 } + ( -36 + 10 ) x - 40 \\
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F & = & 9 x^{ 2 } - 26 x - 40
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\end{eqnarray*}
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\end{solution}
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\end{parts}
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\question
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Developper et reduire les expressions suivantes.
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\begin{parts}
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\part $A = ( 3 x + 4 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( 3 x + 4 )^{ 2 } \\
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A & = & ( 3 x + 4 ) ( 3 x + 4 ) \\
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A & = & 3 \times 3 x^{ 2 } + ( 4 \times 3 + 3 \times 4 ) x + 4 \times 4 \\
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A & = & 9 x^{ 2 } + ( 12 + 12 ) x + 16 \\
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A & = & 9 x^{ 2 } + 24 x + 16
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\end{eqnarray*}
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\end{solution}
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\part $B = ( 10 x + 8 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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B & = & ( 10 x + 8 )^{ 2 } \\
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B & = & ( 10 x + 8 ) ( 10 x + 8 ) \\
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B & = & 10 \times 10 x^{ 2 } + ( 8 \times 10 + 10 \times 8 ) x + 8 \times 8 \\
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B & = & 100 x^{ 2 } + ( 80 + 80 ) x + 64 \\
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B & = & 100 x^{ 2 } + 160 x + 64
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\end{eqnarray*}
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\end{solution}
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\part $C = ( 6 x - 6 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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C & = & ( 6 x - 6 )^{ 2 } \\
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C & = & ( 6 x - 6 ) ( 6 x - 6 ) \\
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C & = & 6 \times 6 x^{ 2 } + ( -6 \times 6 + 6 \times ( -6 ) ) x - 6 \times ( -6 ) \\
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C & = & 36 x^{ 2 } + ( -36 - 36 ) x + 36 \\
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C & = & 36 x^{ 2 } - 72 x + 36
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\end{eqnarray*}
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\end{solution}
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\part $D = ( 9 x - 10 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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D & = & ( 9 x - 10 )^{ 2 } \\
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D & = & ( 9 x - 10 ) ( 9 x - 10 ) \\
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D & = & 9 \times 9 x^{ 2 } + ( -10 \times 9 + 9 \times ( -10 ) ) x - 10 \times ( -10 ) \\
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D & = & 81 x^{ 2 } + ( -90 - 90 ) x + 100 \\
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D & = & 81 x^{ 2 } - 180 x + 100
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\end{eqnarray*}
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\end{solution}
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\part $E = ( 2 x + 6 ) ( 2 x - 6 )$
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\begin{solution}
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\begin{eqnarray*}
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E & = & ( 2 x + 6 ) ( 2 x - 6 ) \\
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E & = & 2 \times 2 x^{ 2 } + ( 6 \times 2 + 2 \times ( -6 ) ) x + 6 \times ( -6 ) \\
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E & = & 4 x^{ 2 } + ( 12 - 12 ) x - 36 \\
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E & = & 4 x^{ 2 } - 36
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\end{eqnarray*}
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\end{solution}
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\part $F = ( 8 x + 10 ) ( 8 x - 10 )$
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\begin{solution}
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\begin{eqnarray*}
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F & = & ( 8 x + 10 ) ( 8 x - 10 ) \\
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F & = & 8 \times 8 x^{ 2 } + ( 10 \times 8 + 8 \times ( -10 ) ) x + 10 \times ( -10 ) \\
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F & = & 64 x^{ 2 } + ( 80 - 80 ) x - 100 \\
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F & = & 64 x^{ 2 } - 100
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\end{eqnarray*}
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\end{solution}
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\part $G = ( 9 x + 7 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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G & = & ( 9 x + 7 )^{ 2 } \\
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G & = & ( 9 x + 7 ) ( 9 x + 7 ) \\
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G & = & 9 \times 9 x^{ 2 } + ( 7 \times 9 + 9 \times 7 ) x + 7 \times 7 \\
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G & = & 81 x^{ 2 } + ( 63 + 63 ) x + 49 \\
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G & = & 81 x^{ 2 } + 126 x + 49
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\end{eqnarray*}
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\end{solution}
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\part $H = ( 4 x - 10 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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H & = & ( 4 x - 10 )^{ 2 } \\
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H & = & ( 4 x - 10 ) ( 4 x - 10 ) \\
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H & = & 4 \times 4 x^{ 2 } + ( -10 \times 4 + 4 \times ( -10 ) ) x - 10 \times ( -10 ) \\
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H & = & 16 x^{ 2 } + ( -40 - 40 ) x + 100 \\
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H & = & 16 x^{ 2 } - 80 x + 100
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\end{eqnarray*}
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\end{solution}
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\end{parts}
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\end{questions}
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\end{document}
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%%% Local Variables:
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%%% TeX-master: "master"
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%%% End:
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