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

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1. \((b-\frac{-1}{16})(q-\frac{-13}{6})\)
2. \((x+\frac{-9}{20})(b+\frac{15}{4})\)
3. \((\frac{7}{17}-x)(\frac{-19}{16}+x)\)
4. \((\frac{-2}{7}-a)(q+\frac{1}{14})\)
5. \((\frac{13}{4}-a)(\frac{-15}{11}+p)\)
6. \((\frac{11}{18}-x)(\frac{20}{11}+a)\)
7. \((q+\frac{-13}{17})(\frac{12}{8}+p)\)
8. \((\frac{2}{7}-a)(x-\frac{18}{14})\)
9. \((\frac{-3}{13}-q)(11-b)\)
10. \((\frac{6}{9}+x)(\frac{-16}{14}-b)\)
11. \((b-\frac{2}{18})(\frac{-15}{7}-x)\)
12. \((\frac{17}{15}+p)(q-\frac{-14}{11})\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{-1}{16})(q-\frac{-13}{6})& =(\color{red}{b}+\color{orange}{\frac{1}{16}}).(\color{green}{q}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{1}{16})} . \color{green}{(q)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{6}b+\frac{1}{16}q+\frac{1}{16}.\frac{13}{6}& \text{Uitwerken } \\ & =bq+\frac{13}{6}b+\frac{1}{16}q+\frac{13}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{-9}{20})(b+\frac{15}{4})& =(\color{red}{x}+\color{orange}{\frac{-9}{20}}).(\color{green}{b}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{4}x-\frac{9}{20}b-\frac{9}{20}.\frac{15}{4}& \text{Uitwerken } \\ & =bx+\frac{15}{4}x-\frac{9}{20}b-\frac{135}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{15}{4}x-\frac{9}{20}b-\frac{27}{16} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{7}{17}-x)(\frac{-19}{16}+x)& =(\color{red}{-x}+\color{orange}{\frac{7}{17}}).(\color{green}{x}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{7}{17})} . \color{green}{(x)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{19}{16}x+\frac{7}{17}x-\frac{7}{17}.\frac{19}{16}& \text{Uitwerken } \\ & =-x^2+(\frac{19}{16}+\frac{7}{17})x-\frac{133}{272} & \text{Neem samen} \\ &=-x^2+\frac{435}{272}x-\frac{133}{272} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{-2}{7}-a)(q+\frac{1}{14})& =(\color{red}{-a}+\color{orange}{\frac{-2}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{14}a-\frac{2}{7}q-\frac{2}{7}.\frac{1}{14}& \text{Uitwerken } \\ & =-aq-\frac{1}{14}a-\frac{2}{7}q-\frac{2}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{1}{14}a-\frac{2}{7}q-\frac{1}{49} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{13}{4}-a)(\frac{-15}{11}+p)& =(\color{red}{-a}+\color{orange}{\frac{13}{4}}).(\color{green}{p}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{13}{4})} . \color{green}{(p)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{15}{11}a+\frac{13}{4}p-\frac{13}{4}.\frac{15}{11}& \text{Uitwerken } \\ & =-ap+\frac{15}{11}a+\frac{13}{4}p-\frac{195}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{11}{18}-x)(\frac{20}{11}+a)& =(\color{red}{-x}+\color{orange}{\frac{11}{18}}).(\color{green}{a}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{11}{18})} . \color{green}{(a)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{20}{11}x+\frac{11}{18}a+\frac{11}{18}.\frac{20}{11}& \text{Uitwerken } \\ & =-ax-\frac{20}{11}x+\frac{11}{18}a+\frac{220}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{20}{11}x+\frac{11}{18}a+\frac{10}{9} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q+\frac{-13}{17})(\frac{12}{8}+p)& =(\color{red}{q}+\color{orange}{\frac{-13}{17}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{2}q-\frac{13}{17}p-\frac{13}{17}.\frac{3}{2}& \text{Uitwerken } \\ & =pq+\frac{3}{2}q-\frac{13}{17}p-\frac{39}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{2}{7}-a)(x-\frac{18}{14})& =(\color{red}{-a}+\color{orange}{\frac{2}{7}}).(\color{green}{x}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{7}a+\frac{2}{7}x-\frac{2}{7}.\frac{9}{7}& \text{Uitwerken } \\ & =-ax+\frac{9}{7}a+\frac{2}{7}x-\frac{18}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-3}{13}-q)(11-b)& =(\color{red}{-q}+\color{orange}{\frac{-3}{13}}).(\color{green}{-b}+\color{blue}{11})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(11)} + \color{orange}{(\frac{-3}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = bq-11q+\frac{3}{13}b-\frac{3}{13}.11& \text{Uitwerken } \\ & =bq-11q+\frac{3}{13}b-\frac{33}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{6}{9}+x)(\frac{-16}{14}-b)& =(\color{red}{x}+\color{orange}{\frac{2}{3}}).(\color{green}{-b}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{8}{7}x-\frac{2}{3}b-\frac{2}{3}.\frac{8}{7}& \text{Uitwerken } \\ & =-bx-\frac{8}{7}x-\frac{2}{3}b-\frac{16}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b-\frac{2}{18})(\frac{-15}{7}-x)& =(\color{red}{b}+\color{orange}{\frac{-1}{9}}).(\color{green}{-x}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{15}{7}b+\frac{1}{9}x+\frac{1}{9}.\frac{15}{7}& \text{Uitwerken } \\ & =-bx-\frac{15}{7}b+\frac{1}{9}x+\frac{15}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{15}{7}b+\frac{1}{9}x+\frac{5}{21} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{17}{15}+p)(q-\frac{-14}{11})& =(\color{red}{p}+\color{orange}{\frac{17}{15}}).(\color{green}{q}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{17}{15})} . \color{green}{(q)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{14}{11}p+\frac{17}{15}q+\frac{17}{15}.\frac{14}{11}& \text{Uitwerken } \\ & =pq+\frac{14}{11}p+\frac{17}{15}q+\frac{238}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)