Fix: modif de Camille et import du remplacer
continuous-integration/drone/push Build is passing Details

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Bertrand Benjamin 2022-09-14 14:33:07 +02:00
parent a9a47368c9
commit fb26e40c59
5 changed files with 58 additions and 51 deletions

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@ -3,15 +3,15 @@
\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 $I = 5x - 3 + 3x^{2} - 5x - 7x^{2}$
\item $A = - 6x - 7 + 10x + 3$
\item $B = - 4t - 3 - 10t - 7t$
\item $C = - 8t - 4 - 3t + 8t$
\item $D = 4x + 5 - 4x - 9$
\item $E = - 7t + 9 + 2t - 9 - 4t$
\item $F = \dfrac{- 9}{9} + 9a + 4a + 8$
\item $G = 6x^{2} + 4 - 2x^{2} + 4 - 5x^{2}$
\item $H = - 9x - 10 - 3x^{2} + 5 - 4x^{2}$
\item $I = - 9x - 5 + 7x^{2} + 9x + 9x^{2}$
\end{enumerate}
\end{multicols}
\end{exercise}
@ -21,55 +21,55 @@
\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
A & = - 6x - 7 + 10x + 3 \\ & = - 6x - 7 + 10x + 3 \\ & = - 6x + 10x - 7 + 3 \\ & = (- 6 + 10) \times x - 4 \\ & = 4x - 4
\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
B & = - 4t - 3 - 10t - 7t \\ & = - 4t - 3 + (- 10 - 7) \times t \\ & = - 4t - 3 - 17t \\ & = - 4t - 17t - 3 \\ & = (- 4 - 17) \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
C & = - 8t - 4 - 3t + 8t \\ & = - 8t - 4 + (- 3 + 8) \times t \\ & = - 8t - 4 + 5t \\ & = - 8t + 5t - 4 \\ & = (- 8 + 5) \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
D & = 4x + 5 - 4x - 9 \\ & = 4x + 5 - 4x - 9 \\ & = 4x - 4x + 5 - 9 \\ & = (4 - 4) \times x - 4 \\ & = 0x - 4 \\ & = - 4
\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
E & = - 7t + 9 + 2t - 9 - 4t \\ & = - 7t + 9 + (2 - 4) \times t - 9 \\ & = - 7t + 9 - 9 - 2t \\ & = (- 7 - 2) \times t + 0 \\ & = - 9t
\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}
F & = \dfrac{- 9}{9} + 9a + 4a + 8 \\ & = 9a + \dfrac{- 9}{9} + 4a + 8 \\ & = 9a + 4a + \dfrac{- 9}{9} + 8 \\ & = (9 + 4) \times a + \dfrac{- 9}{9} + \dfrac{8}{1} \\ & = 13a + \dfrac{- 9}{9} + \dfrac{8 \times 9}{1 \times 9} \\ & = 13a + \dfrac{- 9}{9} + \dfrac{72}{9} \\ & = 13a + \dfrac{- 9}{9} + \dfrac{72}{9} \\ & = 13a + \dfrac{- 9 + 72}{9} \\ & = 13a + \dfrac{63}{9}
\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
G & = 6x^{2} + 4 - 2x^{2} + 4 - 5x^{2} \\ & = 6x^{2} + 4 + (- 2 - 5) \times x^{2} + 4 \\ & = 6x^{2} + 4 + 4 - 7x^{2} \\ & = (6 - 7) \times x^{2} + 8 \\ & = - x^{2} + 8
\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
H & = - 9x - 10 - 3x^{2} + 5 - 4x^{2} \\ & = - 3x^{2} - 9x - 10 + 5 - 4x^{2} \\ & = - 3x^{2} - 4x^{2} - 9x - 10 + 5 \\ & = (- 3 - 4) \times x^{2} - 9x - 5 \\ & = - 7x^{2} - 9x - 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
I & = - 9x - 5 + 7x^{2} + 9x + 9x^{2} \\ & = 7x^{2} - 9x - 5 + 9x + 9x^{2} \\ & = 7x^{2} + 9x^{2} - 9x + 9x - 5 \\ & = (7 + 9) \times x^{2} + (- 9 + 9) \times x - 5 \\ & = 16x^{2} - 5
\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
Développer puis 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 $F = \dfrac{9}{4} \times x(2x + 8)$
\item $A = - 6(3x - 7)$
\item $B = - 6(- 7 + 3t)$
\item $C = t(7 - 5t)$
\item $D = 10x(4x + 7)$
\item $E = - 3x(- 5x - 4)$
\item $F = \dfrac{2}{10} \times x(2x + 9)$
\end{enumerate}
\end{multicols}
\end{exercise}
@ -79,45 +79,45 @@
\begin{enumerate}
\item
\begin{align*}
A & = 10(- 8x + 8) \\ & = 10 \times - 8x + 10 \times 8 \\ & = 10(- 8) \times x + 80 \\ & = - 80x + 80
A & = - 6(3x - 7) \\ & = - 6 \times 3x - 6(- 7) \\ & = - 6 \times 3 \times x + 42 \\ & = - 18x + 42
\end{align*}
\item
\begin{align*}
B & = 7(- 4 + 8t) \\ & = 7 \times 8t + 7(- 4) \\ & = 7 \times 8 \times t - 28 \\ & = 56t - 28
B & = - 6(- 7 + 3t) \\ & = - 6 \times 3t - 6(- 7) \\ & = - 6 \times 3 \times t + 42 \\ & = - 18t + 42
\end{align*}
\item
\begin{align*}
C & = t(3 + 7t) \\ & = t \times 7t + t \times 3 \\ & = 7t^{2} + 3t
C & = t(7 - 5t) \\ & = t \times - 5t + t \times 7 \\ & = - 5t^{2} + 7t
\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
D & = 10x(4x + 7) \\ & = 10x \times 4x + 10x \times 7 \\ & = 10 \times 4 \times x^{1 + 1} + 7 \times 10 \times x \\ & = 40x^{2} + 70x
\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
E & = - 3x(- 5x - 4) \\ & = - 3x \times - 5x - 3x(- 4) \\ & = - 3(- 5) \times x^{1 + 1} - 4(- 3) \times x \\ & = 15x^{2} + 12x
\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
F & = \dfrac{2}{10} \times x(2x + 9) \\ & = \dfrac{2}{10} \times x \times 2x + \dfrac{2}{10} \times x \times 9 \\ & = \dfrac{2}{10} \times 2 \times x^{1 + 1} + 9 \times \dfrac{2}{10} \times x \\ & = \dfrac{2 \times 2}{10} \times x^{2} + \dfrac{9 \times 2}{10} \times x \\ & = \dfrac{4}{10} \times x^{2} + \dfrac{18}{10} \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
Développer puis 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 $H = (\dfrac{- 6}{4} \times x - 7)^{2}$
\item $A = (- 10x - 9)(3x - 5)$
\item $B = (8t - 6)(4t - 2)$
\item $C = (2x + 6)(- 6x - 7)$
\item $D = (2x - 9)(2x + 8)$
\item $E = (- 3x + 2)^{2}$
\item $F = (8x + 5)^{2}$
\item $G = (8x + 5)^{2}$
\item $H = (\dfrac{10}{7} \times x - 10)^{2}$
\end{enumerate}
\end{multicols}
\end{exercise}
@ -127,35 +127,35 @@
\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
A & = (- 10x - 9)(3x - 5) \\ & = - 10x \times 3x - 10x(- 5) - 9 \times 3x - 9(- 5) \\ & = - 10 \times 3 \times x^{1 + 1} - 5(- 10) \times x - 9 \times 3 \times x + 45 \\ & = 50x - 27x - 30x^{2} + 45 \\ & = (50 - 27) \times x - 30x^{2} + 45 \\ & = - 30x^{2} + 23x + 45
\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
B & = (8t - 6)(4t - 2) \\ & = 8t \times 4t + 8t(- 2) - 6 \times 4t - 6(- 2) \\ & = 8 \times 4 \times t^{1 + 1} - 2 \times 8 \times t - 6 \times 4 \times t + 12 \\ & = - 16t - 24t + 32t^{2} + 12 \\ & = (- 16 - 24) \times t + 32t^{2} + 12 \\ & = 32t^{2} - 40t + 12
\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
C & = (2x + 6)(- 6x - 7) \\ & = 2x \times - 6x + 2x(- 7) + 6 \times - 6x + 6(- 7) \\ & = 2(- 6) \times x^{1 + 1} - 7 \times 2 \times x + 6(- 6) \times x - 42 \\ & = - 14x - 36x - 12x^{2} - 42 \\ & = (- 14 - 36) \times x - 12x^{2} - 42 \\ & = - 12x^{2} - 50x - 42
\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
D & = (2x - 9)(2x + 8) \\ & = 2x \times 2x + 2x \times 8 - 9 \times 2x - 9 \times 8 \\ & = 2 \times 2 \times x^{1 + 1} + 8 \times 2 \times x - 9 \times 2 \times x - 72 \\ & = 16x - 18x + 4x^{2} - 72 \\ & = (16 - 18) \times x + 4x^{2} - 72 \\ & = 4x^{2} - 2x - 72
\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
E & = (- 3x + 2)^{2} \\ & = (- 3x + 2)(- 3x + 2) \\ & = - 3x \times - 3x - 3x \times 2 + 2 \times - 3x + 2 \times 2 \\ & = - 3(- 3) \times x^{1 + 1} + 2(- 3) \times x + 2(- 3) \times x + 4 \\ & = - 6x - 6x + 9x^{2} + 4 \\ & = (- 6 - 6) \times x + 9x^{2} + 4 \\ & = 9x^{2} - 12x + 4
\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
F & = (8x + 5)^{2} \\ & = (8x + 5)(8x + 5) \\ & = 8x \times 8x + 8x \times 5 + 5 \times 8x + 5 \times 5 \\ & = 8 \times 8 \times x^{1 + 1} + 5 \times 8 \times x + 5 \times 8 \times x + 25 \\ & = 40x + 40x + 64x^{2} + 25 \\ & = (40 + 40) \times x + 64x^{2} + 25 \\ & = 64x^{2} + 80x + 25
\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
G & = (8x + 5)^{2} \\ & = (8x + 5)(8x + 5) \\ & = 8x \times 8x + 8x \times 5 + 5 \times 8x + 5 \times 5 \\ & = 8 \times 8 \times x^{1 + 1} + 5 \times 8 \times x + 5 \times 8 \times x + 25 \\ & = 40x + 40x + 64x^{2} + 25 \\ & = (40 + 40) \times x + 64x^{2} + 25 \\ & = 64x^{2} + 80x + 25
\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
H & = (\dfrac{10}{7} \times x - 10)^{2} \\ & = (\dfrac{10}{7} \times x - 10)(\dfrac{10}{7} \times x - 10) \\ & = \dfrac{10}{7} \times x \times \dfrac{10}{7} \times x + \dfrac{10}{7} \times x(- 10) - 10 \times \dfrac{10}{7} \times x - 10(- 10) \\ & = \dfrac{10}{7} \times \dfrac{10}{7} \times x^{1 + 1} - 10 \times \dfrac{10}{7} \times x - 10 \times \dfrac{10}{7} \times x + 100 \\ & = \dfrac{- 10 \times 10}{7} \times x + \dfrac{- 10 \times 10}{7} \times x + \dfrac{10 \times 10}{7 \times 7} \times x^{2} + 100 \\ & = \dfrac{- 100}{7} \times x + \dfrac{100}{49} \times x^{2} + \dfrac{- 100}{7} \times x + 100 \\ & = 100 + \dfrac{100}{49} \times x^{2} + \dfrac{- 100}{7} \times x + \dfrac{- 100}{7} \times x \\ & = 100 + \dfrac{100}{49} \times x^{2} + (\dfrac{- 100}{7} + \dfrac{- 100}{7}) \times x \\ & = 100 + \dfrac{100}{49} \times x^{2} + \dfrac{- 100 - 100}{7} \times x \\ & = \dfrac{100}{49} \times x^{2} + \dfrac{- 200}{7} \times x + 100
\end{align*}
\end{enumerate}
\end{multicols}

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@ -2,7 +2,7 @@ Calcul littéral
###############
:date: 2022-09-13
:modified: 2022-09-13
:modified: 2022-09-14
:authors: Benjamin Bertrand
:tags: Calcul littéral
:category: 2nd
@ -22,3 +22,10 @@ La solution des exercices techniques
.. image:: ./solutions.pdf
:height: 200px
:alt: Les solutions
Exercices pour remplacer dans une formule
.. image:: ./3E_remplacer_dans_formules.pdf
:height: 200px
:alt: Exercices pour remplacer dans une formule

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@ -36,7 +36,7 @@
\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
Développer puis réduire les expressions suivantes
\Block{
set reduction = {
"A": random_expression("{a}({c}x + {d})", global_config={"rejected":[1, 0, -1]}),
@ -70,7 +70,7 @@
\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
Développer puis réduire les expressions suivantes
\Block{
set reduction = {
"A": random_expression("({a}x + {b})({c}x + {d})", global_config={"rejected":[1, 0, -1]}),