Lösung 2.1:1b

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