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\begin{center}\section*{\textcolor{red}{2\up{nde} : correction de l'accompagnement personnalisé (séance 12 du 12/12/2023)}}\end{center}



\subsection{}
Développer, puis réduire, si possible, chaque expression :


\begin{enumerate}
\item $A(x)=2x(x + 3)=2x\times x+2x\times 3=\boxed{\textcolor{red}{2x^2+6x}}$

\item $B(y)=-7y^2\left(-5 - 2y^2\right) =7y^2\times 5+7y^2\times 2y^2=35y^2+14y^4=\boxed{\textcolor{red}{14y^4+35y^2}}$

\item $C(x)= (x + 5)(x + 1)=x\times x+x\times 1+5\times x5\times 1=x^2+x+5x+5=\boxed{\textcolor{red}{x^2+6x+5}}$

\item $D(x)=(2x - 5) (x + 4)=2x\times x+2x\times 4-5\times x-5\times 4=2x^2+8x-5x-20=\boxed{\textcolor{red}{2x^2+3x-20}}$

\item $E(x)=(x + 4)(x - 6) + (-1 + x)(x - 7)\\
=\left[x^2-6x+4x-24\right]+\left[-x+7+x^2-7x\right]\\
=\left(x^2-2x-24\right)+\left(x^2-8x+7\right)\\
=x^2-2x-24+x^2-8x+7=\boxed{\textcolor{red}{2x^2-10x-17}}$

\item $F(a)=-3\left(a^2 + 2\right) - (a - 3)(2a + 7)\\
=-3a^2-6-\left[2a^2+7a-6a-21\right]\\
=-3a^2-6-2a^2-7a+6a+21\\
=\boxed{\textcolor{red}{-5a^2-a+15}}$
\end{enumerate}

\subsection{}
Développer et réduire

\begin{enumerate}
\item $A(x)=5x(x - 1) + 3x =5x^2-5x+3x=\boxed{\textcolor{red}{5x^2-2x}}$

\item $B(x)=(x - 2)(x + 3) =x^2+3x-2x-6=\boxed{\textcolor{red}{x^2+x-6}}$

\item $C(x)=(6x + 7)(3x - 1) =18x^2-6x+21x-7=\boxed{\textcolor{red}{18x^2+15x-7}}$

\item  $D(y)=(y + 1)(y - 3) + (y - 1)(y + 5) =\left[y^2-3y+y-7\right]+\left[y^2+5y-y-5\right]=y^2-2y-7+y^2+4y-5\\
=\boxed{\textcolor{red}{2y^2+2y-12}}$

\item  $E(y)=5(x - y) + y(8 - x) + x(y + 3) =5x-5y+8y-xy+xy+3x=\boxed{\textcolor{red}{8x+3y}}$

\item  $F(d)=(d - 3)(d + 1) - (d + 4)(d - 1) =\left[d^2+d-3d-3\right]-\left[d^2-d+4d-4\right]=\left[d^2-2d-3\right]-\left[d^2+3d-4\right]\\
=d^2-2d-3-d^2-3d+4=\boxed{\textcolor{red}{-5d+1}}$

\end{enumerate}

\label{fin}
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