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

Werk uit en vereenvoudig

\((b+\frac{-1}{20})(\frac{-12}{20}-b)\)

\(\begin{align}(b+\frac{-1}{20})(\frac{-12}{20}-b)& =(\color{red}{b}+\color{orange}{\frac{-1}{20}}).(\color{green}{-b}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-1}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{3}{5}b+\frac{1}{20}b+\frac{1}{20}.\frac{3}{5}& \text{Uitwerken } \\ & =-b^2+((\frac{-3}{5})+\frac{1}{20})b+(\frac{-3}{100}) & \text{Neem samen} \\ &=-b^2-\frac{11}{20}b+(\frac{-3}{100}) & \text{Maak de som} \\\end{align}\)