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

Werk uit en vereenvoudig

\((\frac{-15}{12}-p)(\frac{18}{19}+b)\)

\(\begin{align}(\frac{-15}{12}-p)(\frac{18}{19}+b)& =(\color{red}{-p}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{18}{19}p-\frac{5}{4}b-\frac{5}{4}.\frac{18}{19}& \text{Uitwerken } \\ & =-bp-\frac{18}{19}p-\frac{5}{4}b-\frac{90}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{18}{19}p-\frac{5}{4}b-\frac{45}{38} & \text{Vereenvoudig} \\\end{align}\)