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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{4}{5})(\frac{11}{20}+q)& =(\color{red}{a}+\color{orange}{\frac{4}{5}}).(\color{green}{q}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{20}a+\frac{4}{5}q+\frac{4}{5}.\frac{11}{20}& \text{Uitwerken } \\ & =aq+\frac{11}{20}a+\frac{4}{5}q+\frac{44}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{11}{20}a+\frac{4}{5}q+\frac{11}{25} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p-\frac{13}{20})(x+\frac{-17}{5})& =(\color{red}{p}+\color{orange}{\frac{-13}{20}}).(\color{green}{x}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{5}p-\frac{13}{20}x+\frac{13}{20}.\frac{17}{5}& \text{Uitwerken } \\ & =px-\frac{17}{5}p-\frac{13}{20}x+\frac{221}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{6}+b)(\frac{-8}{6}-a)& =(\color{red}{b}+\color{orange}{\frac{-11}{6}}).(\color{green}{-a}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{3}b+\frac{11}{6}a+\frac{11}{6}.\frac{4}{3}& \text{Uitwerken } \\ & =-ab-\frac{4}{3}b+\frac{11}{6}a+\frac{44}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{4}{3}b+\frac{11}{6}a+\frac{22}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{1}{5})(q+(-17))& =(\color{red}{p}+\color{orange}{\frac{-1}{5}}).(\color{green}{q}+\color{blue}{(-17)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-17)} + \color{orange}{(\frac{-1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(-17)}& \text{Boogjes en uitschrijven} \\ & = pq-17p-\frac{1}{5}q+\frac{1}{5}.17& \text{Uitwerken } \\ & =pq-17p-\frac{1}{5}q+\frac{17}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{2}{17})(a+\frac{-17}{10})& =(\color{red}{a}+\color{orange}{\frac{-2}{17}}).(\color{green}{a}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{17}{10}a-\frac{2}{17}a+\frac{2}{17}.\frac{17}{10}& \text{Uitwerken } \\ & =a^2+((\frac{-17}{10})+(\frac{-2}{17}))a+\frac{34}{170} & \text{Neem samen} \\ &=a^2-\frac{309}{170}a+\frac{34}{170} & \text{Maak de som} \\ &=a^2-\frac{309}{170}a+\frac{1}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-8}{17})(p+\frac{14}{8})& =(\color{red}{x}+\color{orange}{\frac{-8}{17}}).(\color{green}{p}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{4}x-\frac{8}{17}p-\frac{8}{17}.\frac{7}{4}& \text{Uitwerken } \\ & =px+\frac{7}{4}x-\frac{8}{17}p-\frac{56}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{7}{4}x-\frac{8}{17}p-\frac{14}{17} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{14}{16})(p+\frac{2}{12})& =(\color{red}{x}+\color{orange}{\frac{-7}{8}}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{6}x-\frac{7}{8}p-\frac{7}{8}.\frac{1}{6}& \text{Uitwerken } \\ & =px+\frac{1}{6}x-\frac{7}{8}p-\frac{7}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-9}{4})(a-\frac{12}{11})& =(\color{red}{p}+\color{orange}{\frac{9}{4}}).(\color{green}{a}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(\frac{9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{12}{11}p+\frac{9}{4}a-\frac{9}{4}.\frac{12}{11}& \text{Uitwerken } \\ & =ap-\frac{12}{11}p+\frac{9}{4}a-\frac{108}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{12}{11}p+\frac{9}{4}a-\frac{27}{11} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{16}{20})(\frac{-13}{4}+p)& =(\color{red}{x}+\color{orange}{\frac{-4}{5}}).(\color{green}{p}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{4}x-\frac{4}{5}p+\frac{4}{5}.\frac{13}{4}& \text{Uitwerken } \\ & =px-\frac{13}{4}x-\frac{4}{5}p+\frac{52}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{13}{4}x-\frac{4}{5}p+\frac{13}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{18}-q)(x-\frac{-12}{17})& =(\color{red}{-q}+\color{orange}{\frac{1}{6}}).(\color{green}{x}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{12}{17}q+\frac{1}{6}x+\frac{1}{6}.\frac{12}{17}& \text{Uitwerken } \\ & =-qx-\frac{12}{17}q+\frac{1}{6}x+\frac{12}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{12}{17}q+\frac{1}{6}x+\frac{2}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a-\frac{20}{4})(p+\frac{3}{18})& =(\color{red}{a}+\color{orange}{(-5)}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(-5)} . \color{green}{(p)} + \color{orange}{(-5)} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{6}a-5p-5.\frac{1}{6}& \text{Uitwerken } \\ & =ap+\frac{1}{6}a-5p-\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-1}{12}-x)(\frac{-17}{5}+q)& =(\color{red}{-x}+\color{orange}{\frac{-1}{12}}).(\color{green}{q}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{-1}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{12})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{17}{5}x-\frac{1}{12}q+\frac{1}{12}.\frac{17}{5}& \text{Uitwerken } \\ & =-qx+\frac{17}{5}x-\frac{1}{12}q+\frac{17}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-11 18:06:48
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