Aus Online Mathematik Brückenkurs 1

When the factor \displaystyle xy is multiplied by the expression inside the brackets, \displaystyle 1+x+x^2 , the distributive rule gives that all three terms \displaystyle 1, \displaystyle x and \displaystyle -x^2 are multiplied by \displaystyle xy,

\displaystyle \begin{align} (1+x-x^2)xy &= 1 \cdot xy + x \cdot xy -x^2 \cdot xy\\ &= xy+x^2y-x^3y\,\textrm{.} \end{align}