-
$A(x) = (x+5)^2$
Corrigé
\[\begin{aligned}
A(x)&=(x+5)^2&
\\
&=x^2 + 2\cdot 5\cdot x + 5^2&
\\
&=\boxed{x^2 + 10x + 25}&
\end{aligned}\]
-
$B(x) = (2x-7)^2$
Corrigé
\[\begin{aligned}
B(x) &= (2x-7)^2&
\\
&=(2x)^2 - 2\cdot 7 \cdot 2x + (7)^2&
\\
&= \boxed{4x^2 - 28x + 49}&
\end{aligned}\]
-
$C(x) = (2x+1)(3x-4)^2$
Corrigé
\[\begin{aligned}
C(x) &= (2x+1)(3x-4)^2&
\\
&=(2x+1)\left((3x)^2 - 2\cdot 3x \cdot 4 + 4^2\right)&
\\
&=(2x-1)\left(9x^2 -24x + 16\right)&
\\
&=2x\cdot9x^2 + 2x\cdot(-24x) + 2x\cdot 16 -1\cdot 9x^2 - 1\cdot (-24x) - 1\cdot 16&
\\
&=18x^3 - 48x^2 + 32x - 9x^2 + 24x - 16&
\\
&=\boxed{18x^3 -57x^2 + 56x - 16}&
\end{aligned}\]