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Développer et réduire chacune des expressions suivantes :
\[
A(x) = x - 4(3x - 2).
\]
Corrigé
\[\begin{aligned}
A(x)&= x - 4(3x - 2)&\\
&= x - 4\cdot 3x - 4 \cdot (-2)&\\
&= x - 12x + 8&\\
&= -11x + 8.&
\end{aligned}\]
\[
B(x) = (x-2)(x-3).
\]
Corrigé
\[\begin{aligned}
B(x)&=(x-2)(x-3)&\\
&= x \cdot x + x \cdot (-3) - 2\cdot x - 2 \cdot (-3)&\\
&=x^2 -3x -2x + 6&\\
&= x^2 - 5x + 6.&
\end{aligned}\]
\[
C(x)=6 - 3(2x - 1).
\]
Corrigé
\[\begin{aligned}
C(x)
&= 6 - 3(2x - 1)&\\
&=6 - 3\cdot (2x) - 3 \cdot (-1)&\\
&=6 - 6x + 3&\\
&=9 - 6x.&
\end{aligned}\]
\[
D(x)=(5x-4)(3x + 2).
\]
Corrigé
\[\begin{aligned}
D(x)
&=(5x-4)(3x +2)&\\
&= 5x\cdot 3x + 5x\cdot 2 - 4\cdot 3x - 4\cdot 2&\\
&=15x^2 + 10x - 12x - 8&\\
&= 15x^2 - 2x - 8.&
\end{aligned}\]
\[
E(x)=3\left(x - \frac 1 3\right).
\]
Corrigé
\[\begin{aligned}
E(x)
&=3\left(x - \frac 1 3\right)&\\
&= 3\cdot x + 3\cdot\left(-\frac 1 3\right)&\\
&=3x - 1.&
\end{aligned}\]
\[
F(x)=2x\left(\frac 1 2 x + 1\right).
\]
Corrigé
\[\begin{aligned}
F(x)
&=2x\left(\frac 1 2 x + 1\right)&\\
&=2x\cdot\frac 1 2x + 2x \cdot 1&\\
&=x^2 + 2x.&
\end{aligned}\]
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