retour
Développer et réduire les expressions suivantes :
-
$E(x) = (2x + 1)(x - 3)$
Corrigé
\[\begin{aligned}
E(x)&=(2x+1)(x-3)&
\\
&=2x \cdot x + 2x \cdot(-3) + 1 \cdot x + 1\cdot (-3)&
\\
&= 2x^2 - 6x + x - 3&
\\
&= \boxed{2x^2 - 5x - 3}&
\end{aligned}\]
-
$F(x) = \left(x + 3\right)^2$
Corrigé
\[\begin{aligned}
F(x)&=(x+3)^2&
\\
&=x^2 + 2 \cdot x \cdot 3 + 3^2&
\\
&= \boxed{x^2 + 6x + 9}&
\end{aligned}\]
-
$G(x) = (2x - 5)^2$
Corrigé
\[\begin{aligned}
G(x)&=(2x-5)^2&
\\
&=(2x)^2 - 2\cdot 2x \cdot 5 + 5^2&
\\
&= \boxed{4x^2 - 20x + 25}&
\end{aligned}\]
-
$H(x) = \left(\dfrac 1 2 x + 1\right)\left(x - \dfrac 3 4\right)$
Corrigé
\[\begin{aligned}
H(x)&=\left(\dfrac 1 2 x + 1\right)\left(x - \dfrac 3 4\right)&
\\
&=\dfrac 1 2 x \cdot x + \dfrac 1 2 x \cdot \left(-\dfrac 3 4\right)
+ 1 \cdot x + 1 \cdot \left(-\dfrac 3 4\right)&
\\
&=\dfrac 1 2 x^2 - \dfrac 3 8 x + x - \dfrac 3 4&
\\
&=\boxed{\dfrac 1 2 x^2 + \dfrac 5 8 x - \dfrac 3 4.}&
\end{aligned}\]
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