Pluggakuten.se / Formelsamling / Matematik / Blandade formler

Formel	Anmärkning
$(a+b)^{2} = a^{2}+2ab+b^{2}$	Kvadratregeln
$(a-b)^{2} = a^{2}-2ab+b^{2}$	Kvadratregeln
$a^{2}-b^{2} = (a-b)(a+b)$	Konjugatregeln
$a^{3}+b^{3} = (a+b)(a^2-ab+b^2)$
$a^{3}-b^{3} = (a-b)(a^2+ab+b^2)$


$(a+b)^{n} = a^n +\frac{n}{1!}a^{n-1}\hspace{6}b+\frac{n(n-1)}{2!}a^{n-2}\hspace{6}b^{2}+ \\ +\frac{n(n-1)(n-2)}{3!}a^{n-3} \hspace{6} b^{3}+...+b^{n} = \\ \sum_{k=0}^{n} {n\choose k}a^{n-k}b^k$	Binomialsatsen

Formel	Anmärkning
$\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}$	$b\neq 0$
$\frac{-a}{-b}=\frac{a}{b}$	$b\neq 0$
$a\cdot \frac{b}{c}=a\frac{b}{c}=\frac{ab}{c}$	$c\neq 0$
$\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}$	$b\neq 0, d\neq 0$
$\frac{a}{b}\ / \frac{c}{d}=\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\cdot\frac{d}{c} =\frac{ad}{bc}$	$b\neq 0, c\neq 0, d\neq 0$
$\frac{a}{b} + \frac{c}{d} = \frac{ad}{bd} + \frac{bc}{bd} = \frac{ad+bc}{bd}$	$b\neq 0, d\neq 0$

Rötterna till ekvationen:

ges av: $x_{1,2} = -\frac{p}{2}\pm\sqrt{\left(\frac{p}{2}\right)^2-q}$