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\begin{document}

\begin{center}
\textbf{Formulele inmultirii prescurtate. Puteri}
\end{center}

\begin{enumerate}
\item $(a\pm b)^2=a^2\pm 2ab+b^2$.
\item $a^2-b^2=(a+b)(a-b)$.
\item $(a\pm b)^3=a^3\pm 3a^2b+3ab^2\pm b^3=a^3\pm b^3\pm 3ab(a\pm b)$.
\item $a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2).$
\item $(a_1a_2\dots a_m)^n=a_1^na_2^n\dots a_m^n \qquad m,n\in
        \textbf{N},\ a_i\geq 0,\ i=\overline{1,n}$.
\item $a^{n_1}a^{n_2}\dots a^{n_m}=a^{n_1+n_2+\dots +n_m}
        \qquad m,n\in \textbf{N},\ a\geq 0$.
\item $\ds\frac{a^m}{a^n}=a^{m-n} \qquad  m,n\in \textbf{N},\ a>0$.
\item $(a^m)^n=a^{m\cdot n} \qquad m,n\in \textbf{N},\ a>0$.
\item $\ds a^{-n}=\frac{1}{a^n} \qquad n\in \textbf{N},\ a>0$.
\item $a^{\frac{m}{n}}=\sqrt[n]{a^m}\qquad m,n \in \textbf{N},\ n\geq 2$.
\item $\sqrt[n]{a^m}=
      \left\{
        \begin{array}{l}
          a^\frac{m}{n}, \ \textrm{daca}\ m=2k+1\\[2mm]
          |a|^{\frac{m}{n}}, \ \textrm{daca}\ m=2k
        \end{array}
      \right.
      \qquad k,m,n\in \textbf{N},\ n\geq 2$.
\item $(\sqrt[n]{a})^m=\sqrt[n]{a^m} \qquad m,n\in \textbf{N},\ n\geq 2$.
\item $\sqrt[n]{a_1a_2\dots a_m}=\sqrt[n]{|a_1|}\sqrt[n]{|a_2|}\dots
         \sqrt[n]{|a_m|} \qquad m,n\in \textbf{N},\ n\geq 2$.
\item $\ds\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{|a|}}{\sqrt[n]{|b|}}
         \quad (b\neq 0). \quad
       (\sqrt[n]{a+b}\neq \sqrt[n]{a}+\sqrt[n]{b},\ a\neq 0,\ b\neq 0).
         \qquad n\in \textbf{N},\ n\geq 2$.
\end{enumerate}

\footnotetext[0]{\quad Copyright$\copyright$1999 ONG TCV
    Scoala Virtuala a Tanarului Matematician \quad http://math.ournet.md}

\end{document}
