Klammere $(-1)\backslash left(-1\backslash right)$ aus.

$a+b=-1({\displaystyle \frac{a}{-1}}+{\displaystyle \frac{b}{-1}})=-1(-a-b)a\; +\; b\; =\; -1\; \backslash left(\backslash dfrac\{a\}\{-1\}\; +\; \backslash dfrac\{b\}\{-1\}\backslash right)\; =\; -1\; \backslash left(-a-b\backslash right)$

Klammere $(-1)\backslash left(-1\backslash right)$ aus.

$b-a=-1({\displaystyle \frac{b}{-1}}+{\displaystyle \frac{-a}{-1}})=-1(-b+a)b-a\; =\; -1\; \backslash left(\; \backslash dfrac\{b\}\{-1\}\; +\; \backslash dfrac\{-a\}\{-1\}\backslash right)\; =\; -1\; \backslash left(-b\; +\; a\; \backslash right)$

Klammere $(-1)\backslash left(-1\backslash right)$ aus.

$-a-b-1=-1({\displaystyle \frac{-a}{-1}}+{\displaystyle \frac{-b}{-1}}+{\displaystyle \frac{-1}{-1}})=(a+b+1)-a-b-1\; =\; -1\; \backslash left(\; \backslash dfrac\{-a\}\{-1\}\; +\; \backslash dfrac\{-b\}\{-1\}\; +\; \backslash dfrac\{-1\}\{-1\}\; \backslash right)\; =\; \backslash left(\; a\; +\; b\; +\; 1\backslash right)$

Klammere $(-1)\backslash left(-1\backslash right)$ aus.

$a-b-1=-1({\displaystyle \frac{a}{-1}}+{\displaystyle \frac{-b}{-1}}+{\displaystyle \frac{-1}{-1}})=-1(-a+b+1)a-b-1\; =\; -1\; \backslash left(\; \backslash dfrac\{a\}\{-1\}\; +\; \backslash dfrac\{-b\}\{-1\}\; +\; \backslash dfrac\{-1\}\{-1\}\backslash right)\; =\; -1\; \backslash left(-a\; +b+1\backslash right)$

$-{ab}^4+a^2{b}^3-a^3{b}^2-\{ab\}^4+a^2b^3-a^3b^2$

Suche den Faktor $(-a{b}^2)(-ab^2)$ in jedem Summanden:

$=-{ab}^2\cdot b^2-a\cdot (-{ab}^2)\cdot b+a^2\cdot (-{ab}^2)=\backslash color\{red\}\{-\{ab\}^2\}\; \backslash color\{black\}\backslash cdot\; b^2-\; a\backslash cdot(\backslash color\{red\}\{-\{ab\}^2\}\; \backslash color\{black\})\; \backslash cdot\; b+a^2\backslash cdot(\backslash color\{red\}\{-\{ab\}^2\}\backslash color\{black\}\; )$

Klammere $(-{ab}^2)\backslash left(-\{ab\}^2\backslash right)$ aus.

$=(-{ab}^2)\cdot (b^2-ab+a^2)=(-\{ab\}^2)\backslash cdot\backslash left(b^2-\{ab\}+a^2\backslash right)$

Klammere $(-2ab)\backslash left(-2\{ab\}\backslash right)$ aus.

$2{ab}^2-4a^{2}b=-2ab({\displaystyle \frac{2{ab}^2}{-2ab}}+{\displaystyle \frac{-4a^{2}b}{-2ab}})=-2ab(-b+2a)2\{ab\}^2-4a^2b\; =\; -2\{ab\}\backslash left(\; \backslash dfrac\{2\{ab\}^2\}\{-2\{ab\}\}\; +\backslash dfrac\{-4a^2b\}\{-2\{ab\}\}\; \backslash right)\; =\; -2ab\backslash left(-b+2a\backslash right)$

Klammere $\left({\displaystyle \frac{1}{2}}{x}^{2}y\right)\backslash left(\backslash dfrac12x^2y\backslash right)$ aus.

${\displaystyle \frac{1}{2}}{x}^{4}y-{\displaystyle \frac{5}{2}}{x}^{3}y-x^2{y}^3={\displaystyle \frac{1}{2}}{x}^{2}y({\displaystyle \frac{\frac{1}{2}{x}^{4}y}{\frac{1}{2}{x}^{2}y}}+{\displaystyle \frac{-\frac{5}{2}{x}^{3}y}{\frac{1}{2}{x}^{2}y}}+{\displaystyle \frac{-x^2{y}^3}{\frac{1}{2}{x}^{2}y}})={\displaystyle \frac{1}{2}}{x}^{2}y(x^2-5x-2y^2)\backslash dfrac12x^4y-\backslash dfrac52x^3y-x^2y^3\; =\; \backslash dfrac12x^2y\; \backslash left(\backslash dfrac\{\backslash frac12x^4y\}\{\backslash frac12x^2y\}\; +\; \backslash dfrac\{-\backslash frac52x^3y\}\{\backslash frac12x^2y\}\; +\; \backslash dfrac\{-x^2y^3\}\{\backslash frac12x^2y\}\backslash right)\; =\; \backslash dfrac12x^2y(x^2-5x-2y^2)$