Klammere $(-1)$ aus.

$a+b=-1({\displaystyle \frac{a}{-1}}+{\displaystyle \frac{b}{-1}})=-1(-a-b)$

Klammere $(-1)$ aus.

$b-a=-1({\displaystyle \frac{b}{-1}}+{\displaystyle \frac{-a}{-1}})=-1(-b+a)$

Klammere $(-1)$ aus.

$-a-b-1=-1({\displaystyle \frac{-a}{-1}}+{\displaystyle \frac{-b}{-1}}+{\displaystyle \frac{-1}{-1}})=(a+b+1)$

Klammere $(-1)$ aus.

$a-b-1=-1({\displaystyle \frac{a}{-1}}+{\displaystyle \frac{-b}{-1}}+{\displaystyle \frac{-1}{-1}})=-1(-a+b+1)$

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

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

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

Klammere $(-{ab}^2)$ aus.

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

Klammere $(-2ab)$ aus.

$2{ab}^2-4a^{2}b=-2ab({\displaystyle \frac{2{ab}^2}{-2ab}}+{\displaystyle \frac{-4a^{2}b}{-2ab}})=-2ab(-b+2a)$

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

${\displaystyle \frac{1}{2}}{x}^{4}y-{\displaystyle \frac{5}{2}}{x}^{3}y-x^2{y}^3={\displaystyle \frac{1}{2}}{x}^{2}y({\displaystyle \frac{\frac{1}{2}{x}^{4}y}{\frac{1}{2}{x}^{2}y}}+{\displaystyle \frac{-\frac{5}{2}{x}^{3}y}{\frac{1}{2}{x}^{2}y}}+{\displaystyle \frac{-x^2{y}^3}{\frac{1}{2}{x}^{2}y}})={\displaystyle \frac{1}{2}}{x}^{2}y(x^2-5x-2y^2)$