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

Werk uit en vereenvoudig

\((\frac{11}{9}+a)(\frac{10}{12}+a)\)

\(\begin{align}(\frac{11}{9}+a)(\frac{10}{12}+a)& =(\color{red}{a}+\color{orange}{\frac{11}{9}}).(\color{green}{a}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{11}{9})} . \color{green}{(a)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{6}a+\frac{11}{9}a+\frac{11}{9}.\frac{5}{6}& \text{Uitwerken } \\ & =a^2+(\frac{5}{6}+\frac{11}{9})a+\frac{55}{54} & \text{Neem samen} \\ &=a^2+\frac{37}{18}a+\frac{55}{54} & \text{Maak de som} \\\end{align}\)