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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{8}{3})(\frac{-2}{4}-b)& =(\color{red}{q}+\color{orange}{\frac{-8}{3}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{2}q+\frac{8}{3}b+\frac{8}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =-bq-\frac{1}{2}q+\frac{8}{3}b+\frac{8}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{2}q+\frac{8}{3}b+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a+\frac{18}{10})(\frac{9}{13}-q)& =(\color{red}{a}+\color{orange}{\frac{9}{5}}).(\color{green}{-q}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{9}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{13}a-\frac{9}{5}q+\frac{9}{5}.\frac{9}{13}& \text{Uitwerken } \\ & =-aq+\frac{9}{13}a-\frac{9}{5}q+\frac{81}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{13}{8}-a)(\frac{-10}{17}+p)& =(\color{red}{-a}+\color{orange}{\frac{13}{8}}).(\color{green}{p}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{13}{8})} . \color{green}{(p)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{10}{17}a+\frac{13}{8}p-\frac{13}{8}.\frac{10}{17}& \text{Uitwerken } \\ & =-ap+\frac{10}{17}a+\frac{13}{8}p-\frac{130}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{10}{17}a+\frac{13}{8}p-\frac{65}{68} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q+\frac{10}{7})(\frac{-10}{10}+x)& =(\color{red}{q}+\color{orange}{\frac{10}{7}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1q+\frac{10}{7}x-\frac{10}{7}.1& \text{Uitwerken } \\ & =qx-1q+\frac{10}{7}x-\frac{10}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-5}{11}-b)(a+\frac{15}{3})& =(\color{red}{-b}+\color{orange}{\frac{-5}{11}}).(\color{green}{a}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(5)} + \color{orange}{(\frac{-5}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -ab-5b-\frac{5}{11}a-\frac{5}{11}.5& \text{Uitwerken } \\ & =-ab-5b-\frac{5}{11}a-\frac{25}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{13}+a)(\frac{-11}{6}+p)& =(\color{red}{a}+\color{orange}{\frac{-9}{13}}).(\color{green}{p}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{6}a-\frac{9}{13}p+\frac{9}{13}.\frac{11}{6}& \text{Uitwerken } \\ & =ap-\frac{11}{6}a-\frac{9}{13}p+\frac{99}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{11}{6}a-\frac{9}{13}p+\frac{33}{26} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{5}+a)(\frac{19}{9}-x)& =(\color{red}{a}+\color{orange}{\frac{11}{5}}).(\color{green}{-x}+\color{blue}{\frac{19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{19}{9})} + \color{orange}{(\frac{11}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{19}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{19}{9}a-\frac{11}{5}x+\frac{11}{5}.\frac{19}{9}& \text{Uitwerken } \\ & =-ax+\frac{19}{9}a-\frac{11}{5}x+\frac{209}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{1}{16})(q+\frac{17}{6})& =(\color{red}{b}+\color{orange}{\frac{-1}{16}}).(\color{green}{q}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{6}b-\frac{1}{16}q-\frac{1}{16}.\frac{17}{6}& \text{Uitwerken } \\ & =bq+\frac{17}{6}b-\frac{1}{16}q-\frac{17}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-20}{3})(p+\frac{-17}{6})& =(\color{red}{a}+\color{orange}{\frac{-20}{3}}).(\color{green}{p}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{17}{6}a-\frac{20}{3}p+\frac{20}{3}.\frac{17}{6}& \text{Uitwerken } \\ & =ap-\frac{17}{6}a-\frac{20}{3}p+\frac{340}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{17}{6}a-\frac{20}{3}p+\frac{170}{9} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-17}{18})(a-\frac{-18}{15})& =(\color{red}{a}+\color{orange}{\frac{-17}{18}}).(\color{green}{a}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{6}{5}a-\frac{17}{18}a-\frac{17}{18}.\frac{6}{5}& \text{Uitwerken } \\ & =a^2+(\frac{6}{5}+(\frac{-17}{18}))a-(\frac{-102}{90}) & \text{Neem samen} \\ &=a^2+\frac{23}{90}a-(\frac{-102}{90}) & \text{Maak de som} \\ &=a^2+\frac{23}{90}a+\frac{17}{15} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-5}{13})(q+\frac{-4}{17})& =(\color{red}{p}+\color{orange}{\frac{-5}{13}}).(\color{green}{q}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{17}p-\frac{5}{13}q+\frac{5}{13}.\frac{4}{17}& \text{Uitwerken } \\ & =pq-\frac{4}{17}p-\frac{5}{13}q+\frac{20}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-19}{13}-p)(\frac{4}{7}-q)& =(\color{red}{-p}+\color{orange}{\frac{-19}{13}}).(\color{green}{-q}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{7}p+\frac{19}{13}q-\frac{19}{13}.\frac{4}{7}& \text{Uitwerken } \\ & =pq-\frac{4}{7}p+\frac{19}{13}q-\frac{76}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-08 07:34:12
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