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

$a + b = -1 \left(\dfrac{a}{-1} + \dfrac{b}{-1}\right) = -1 \left(-a-b\right)$

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

$b-a = -1 \left( \dfrac{b}{-1} + \dfrac{-a}{-1}\right) = -1 \left(-b + a \right)$

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

$-a-b-1 = -1 \left( \dfrac{-a}{-1} + \dfrac{-b}{-1} + \dfrac{-1}{-1} \right) = \left( a + b + 1\right)$

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

$a-b-1 = -1 \left( \dfrac{a}{-1} + \dfrac{-b}{-1} + \dfrac{-1}{-1}\right) = -1 \left(-a +b+1\right)$

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

Suche den Faktor $(-ab^2)$ in jedem Summanden:

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

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

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

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

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

Klammere $\left(\dfrac12x^2y\right)$ aus.

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