Mathematik Formelsammlung

$$ Binomische Formel $$¶

\begin{equation} I. (a+b)² = a²+2ab+b² \end{equation} \begin{equation} II. (a-b)² = a²-2ab+b² \end{equation} \begin{equation} III. (a+b)(a-b) = a²-b² \end{equation}

$$ Pythagoras $$¶

\begin{equation} a² + b² = c² \end{equation} \begin{equation} c = \sqrt{a² + b²} \end{equation} \begin{equation} b = \sqrt{c^2 - a^2} \end{equation} \begin{equation} a = \sqrt{c^2 - b^2} \end{equation}

$$ Logarithmus $$¶

\begin{equation} Log_a (xy) = Log_a X + Log_a y \end{equation} \begin{equation} Log_a (\frac xy) = Log_a X - Log_a y \end{equation} \begin{equation} Log_a (x^{y}) = yLog_a X \end{equation} \begin{equation} Log_a \sqrt[n]{x} = \frac 1n Log_a x \end{equation}

$$ Potenzrechnung $$¶

\begin{equation} a^{0} = 1 \end{equation} \begin{equation} a^{n} b^{n} = (ab)^{n} \end{equation} \begin{equation} a^{x} a^{y} = a^{x+y} \end{equation} \begin{equation} (a^{n})^{m} = a^{(nm)} \end{equation}

$$ Wurzelberechnung $$¶

\begin{equation} \sqrt[m]{\sqrt[n]{a}} \space =\space \sqrt[mn]{a} \end{equation} \begin{equation} \sqrt[mn]{a^{mx}} \space =\space \sqrt[n]{a^{x}} \end{equation} \begin{equation} a \sqrt[n]{b} \space =\space \sqrt[n]{a^{n} b} \end{equation} \begin{equation} \sqrt[n]{ab} \space =\space \sqrt[n]{a} \times \sqrt[n]{b} \end{equation}

$$ Quadratische \space Gleichungen $$¶

$$\text Normalform$$ \begin{equation} x² \times px \times q = 0 \end{equation} $$\newline$$ $$\text p,q \space Formel$$ \begin{equation} x_{1,2} = -\frac p2 {\pm} \sqrt {\frac {p^2}4 - {q}} \end{equation}