# Hva er parentesreglene?

Her skal du se på alle parentesreglene samlet sammen.

Regel

### Parenteser

$\begin{array}{llll}\hfill \phantom{\rule{-0.17em}{0ex}}\left(a+b\right)\phantom{\rule{-0.17em}{0ex}}\left(c+d\right)& =a\cdot c+a\cdot d+b\cdot c\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{\rule{2em}{0ex}}+b\cdot d\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill a+\phantom{\rule{-0.17em}{0ex}}\left(c+d\right)& =a+c+d\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill a-\phantom{\rule{-0.17em}{0ex}}\left(c+d\right)& =a-c-d\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill a\cdot \phantom{\rule{-0.17em}{0ex}}\left(b+c\right)& =a\cdot b+a\cdot c\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

$\begin{array}{llll}\hfill \phantom{\rule{-0.17em}{0ex}}\left(a+b\right)\phantom{\rule{-0.17em}{0ex}}\left(c+d\right)& =a\cdot c+a\cdot d+b\cdot c+b\cdot d\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill a+\phantom{\rule{-0.17em}{0ex}}\left(c+d\right)& =a+c+d\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill a-\phantom{\rule{-0.17em}{0ex}}\left(c+d\right)& =a-c-d\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill a\cdot \phantom{\rule{-0.17em}{0ex}}\left(b+c\right)& =a\cdot b+a\cdot c\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

NB! Du må huske å skrive leddene i avtagende eller stigende rekkefølge. Da vil det se slik ut:

Eksempel 1

Regn ut $x+\phantom{\rule{-0.17em}{0ex}}\left(-2x+5\right)$

 $x+\phantom{\rule{-0.17em}{0ex}}\left(-2x+5\right)=x-2x+5=-x+5$

Eksempel 2

Regn ut $4-\phantom{\rule{-0.17em}{0ex}}\left(12-3{x}^{2}\right)$

 $4-\phantom{\rule{-0.17em}{0ex}}\left(12-3{x}^{2}\right)=4-12+3{x}^{2}=3{x}^{2}-8$

Eksempel 3

Regn ut $-4{x}^{2}\phantom{\rule{-0.17em}{0ex}}\left(2-x\right)$

 $-4{x}^{2}\phantom{\rule{-0.17em}{0ex}}\left(2-x\right)=-8{x}^{2}+4{x}^{3}=4{x}^{3}-8{x}^{2}$

Eksempel 4

Regn ut $\phantom{\rule{-0.17em}{0ex}}\left(x+1\right)\phantom{\rule{-0.17em}{0ex}}\left(x-2\right)$

$\begin{array}{llll}\hfill \phantom{\rule{-0.17em}{0ex}}\left(x+1\right)\phantom{\rule{-0.17em}{0ex}}\left(x-2\right)& ={x}^{2}-2x+x-2\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & ={x}^{2}-x-2\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

$\begin{array}{lll}\hfill \phantom{\rule{-0.17em}{0ex}}\left(x+1\right)\phantom{\rule{-0.17em}{0ex}}\left(x-2\right)={x}^{2}-2x+x-2={x}^{2}-x-2& \phantom{\rule{2em}{0ex}}& \hfill \end{array}$

Eksempel 5

Regn ut $\phantom{\rule{-0.17em}{0ex}}\left(3{x}^{2}+y\right)\phantom{\rule{-0.17em}{0ex}}\left(2-x\right)$ $\begin{array}{llll}\hfill \phantom{\rule{-0.17em}{0ex}}\left(3{x}^{2}+y\right)\phantom{\rule{-0.17em}{0ex}}\left(2-x\right)& =6{x}^{2}-3{x}^{3}+2y-xy\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =-3{x}^{3}+6{x}^{2}-xy+2y\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Eksempel 6

Regn ut $\phantom{\rule{-0.17em}{0ex}}\left(2x+3\right)\phantom{\rule{-0.17em}{0ex}}\left(4x-5\right)$

$\begin{array}{llll}\hfill \phantom{\rule{-0.17em}{0ex}}\left(2x+3\right)\phantom{\rule{-0.17em}{0ex}}\left(4x-5\right)& =2x\cdot 4x+2x\cdot \phantom{\rule{-0.17em}{0ex}}\left(-5\right)\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{\rule{2em}{0ex}}+3\cdot 4x+3\cdot \phantom{\rule{-0.17em}{0ex}}\left(-5\right)\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =8{x}^{2}+\phantom{\rule{-0.17em}{0ex}}\left(-10x\right)+12x-15\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =8{x}^{2}+2x-15\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

$\begin{array}{llll}\hfill \phantom{\rule{-0.17em}{0ex}}\left(2x+3\right)\phantom{\rule{-0.17em}{0ex}}\left(4x-5\right)& =2x\cdot 4x+2x\cdot \phantom{\rule{-0.17em}{0ex}}\left(-5\right)+3\cdot 4x+3\cdot \phantom{\rule{-0.17em}{0ex}}\left(-5\right)\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =8{x}^{2}+\phantom{\rule{-0.17em}{0ex}}\left(-10x\right)+12x-15\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =8{x}^{2}+2x-15\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

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Hvordan gange parenteser