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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-8}{4})(\frac{4}{18}-p)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{-p}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(2)} . \color{green}{(-p)} + \color{orange}{(2)} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{9}a-2p+2.\frac{2}{9}& \text{Uitwerken } \\ & =-ap+\frac{2}{9}a-2p+\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{18}{15}+p)(q+\frac{2}{2})& =(\color{red}{p}+\color{orange}{\frac{6}{5}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{6}{5})} . \color{green}{(q)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1p+\frac{6}{5}q+\frac{6}{5}.1& \text{Uitwerken } \\ & =pq+1p+\frac{6}{5}q+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{18}+p)(x-\frac{-13}{4})& =(\color{red}{p}+\color{orange}{\frac{-8}{9}}).(\color{green}{x}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{4}p-\frac{8}{9}x-\frac{8}{9}.\frac{13}{4}& \text{Uitwerken } \\ & =px+\frac{13}{4}p-\frac{8}{9}x-\frac{104}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{13}{4}p-\frac{8}{9}x-\frac{26}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{12}+a)(\frac{7}{13}+x)& =(\color{red}{a}+\color{orange}{\frac{5}{3}}).(\color{green}{x}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{13}a+\frac{5}{3}x+\frac{5}{3}.\frac{7}{13}& \text{Uitwerken } \\ & =ax+\frac{7}{13}a+\frac{5}{3}x+\frac{35}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{14}{11})(a+\frac{11}{10})& =(\color{red}{b}+\color{orange}{\frac{-14}{11}}).(\color{green}{a}+\color{blue}{\frac{11}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{11}{10})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{11}{10})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{10}b-\frac{14}{11}a-\frac{14}{11}.\frac{11}{10}& \text{Uitwerken } \\ & =ab+\frac{11}{10}b-\frac{14}{11}a-\frac{154}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{11}{10}b-\frac{14}{11}a-\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{7}{3}-p)(\frac{14}{20}-p)& =(\color{red}{-p}+\color{orange}{\frac{7}{3}}).(\color{green}{-p}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{7}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{7}{10}p-\frac{7}{3}p+\frac{7}{3}.\frac{7}{10}& \text{Uitwerken } \\ & =p^2+((\frac{-7}{10})+(\frac{-7}{3}))p+\frac{49}{30} & \text{Neem samen} \\ &=p^2-\frac{91}{30}p+\frac{49}{30} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{16}+p)(b-\frac{14}{15})& =(\color{red}{p}+\color{orange}{\frac{-9}{16}}).(\color{green}{b}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{14}{15}p-\frac{9}{16}b+\frac{9}{16}.\frac{14}{15}& \text{Uitwerken } \\ & =bp-\frac{14}{15}p-\frac{9}{16}b+\frac{126}{240} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{14}{15}p-\frac{9}{16}b+\frac{21}{40} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{2}{19}+a)(\frac{-1}{4}-q)& =(\color{red}{a}+\color{orange}{\frac{2}{19}}).(\color{green}{-q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{2}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{4}a-\frac{2}{19}q-\frac{2}{19}.\frac{1}{4}& \text{Uitwerken } \\ & =-aq-\frac{1}{4}a-\frac{2}{19}q-\frac{2}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{1}{4}a-\frac{2}{19}q-\frac{1}{38} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q-\frac{10}{9})(b-\frac{9}{7})& =(\color{red}{q}+\color{orange}{\frac{-10}{9}}).(\color{green}{b}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{9}{7}q-\frac{10}{9}b+\frac{10}{9}.\frac{9}{7}& \text{Uitwerken } \\ & =bq-\frac{9}{7}q-\frac{10}{9}b+\frac{90}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{9}{7}q-\frac{10}{9}b+\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{8}{3}+q)(a-\frac{10}{13})& =(\color{red}{q}+\color{orange}{\frac{8}{3}}).(\color{green}{a}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{8}{3})} . \color{green}{(a)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{10}{13}q+\frac{8}{3}a-\frac{8}{3}.\frac{10}{13}& \text{Uitwerken } \\ & =aq-\frac{10}{13}q+\frac{8}{3}a-\frac{80}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{6}{17}-a)(\frac{11}{7}+a)& =(\color{red}{-a}+\color{orange}{\frac{6}{17}}).(\color{green}{a}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(\frac{6}{17})} . \color{green}{(a)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{11}{7}a+\frac{6}{17}a+\frac{6}{17}.\frac{11}{7}& \text{Uitwerken } \\ & =-a^2+((\frac{-11}{7})+\frac{6}{17})a+(\frac{-66}{119}) & \text{Neem samen} \\ &=-a^2-\frac{145}{119}a+(\frac{-66}{119}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(a-\frac{20}{19})(b+\frac{1}{2})& =(\color{red}{a}+\color{orange}{\frac{-20}{19}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-20}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}a-\frac{20}{19}b-\frac{20}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}a-\frac{20}{19}b-\frac{20}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{2}a-\frac{20}{19}b-\frac{10}{19} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-09 17:18:38
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