Distributiviteit \((a+r)(b+s)\)

Werk uit en vereenvoudig

\((q+\frac{-6}{19})(b+\frac{-6}{9})\)

\(\begin{align}(q+\frac{-6}{19})(b+\frac{-6}{9})& =(\color{red}{q}+\color{orange}{\frac{-6}{19}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-6}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{19})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{3}q-\frac{6}{19}b+\frac{6}{19}.\frac{2}{3}& \text{Uitwerken } \\ & =bq-\frac{2}{3}q-\frac{6}{19}b+\frac{12}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{2}{3}q-\frac{6}{19}b+\frac{4}{19} & \text{Vereenvoudig} \\\end{align}\)