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\newcommand{\mcm}{\mathcal{M}}\newcommand{\mcc}{\mathcal{C}}
\newcommand{\mcmn}{\mathcal{M}}\newcommand{\mcmnr}{\mathcal{M}_n(\mtr)}
\newcommand{\mcmnk}{\mathcal{M}_n(\mtk)}\newcommand{\mcsn}{\mathcal{S}_n}
\newcommand{\mcs}{\mathcal{S}}\newcommand{\mcd}{\mathcal{D}}
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\newcommand{\mnr}{\mathcal{M}_n(\mtr)}\DeclareMathOperator{\ch}{ch}
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\newcommand{\mcun}{\mcu_n}\newcommand{\dis}{\displaystyle}
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\newcommand{\rab}{\mathcal{R}(a,b)}\newcommand{\pss}[2]{\langle #1,#2\rangle}
$$
Bibm@thFormulaire de Mathématiques : identités remarquables
$$(a+b)^2=a^2+2ab+b^2$$
$$(a-b)^2=a^2-2ab+b^2$$
$$(a+b)(a-b)=a^2-b^2$$
$$(a+b)^3=a^3+3a^2b+3ab^2+b^3$$
$$(a-b)^3=a^3-3a^2b+3ab^2-b^3$$
\begin{eqnarray*}
a^n-b^n&=&(a-b)\left(a^{n-1}+a^{n-2}b+\cdots+ab^{n-2}+b^{n-1}\right)\\
&=&(a-b)\sum_{k=0}^{n-1}a^kb^{n-1-k}
\end{eqnarray*}
