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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{16}-q)(\frac{11}{5}-p)& =(\color{red}{-q}+\color{orange}{\frac{-19}{16}}).(\color{green}{-p}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{5}q+\frac{19}{16}p-\frac{19}{16}.\frac{11}{5}& \text{Uitwerken } \\ & =pq-\frac{11}{5}q+\frac{19}{16}p-\frac{209}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{2}+p)(\frac{5}{7}+p)& =(\color{red}{p}+\color{orange}{10}).(\color{green}{p}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(10)} . \color{green}{(p)} + \color{orange}{(10)} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{7}p+10p+10.\frac{5}{7}& \text{Uitwerken } \\ & =p^2+(\frac{5}{7}+10)p+\frac{50}{7} & \text{Neem samen} \\ &=p^2+\frac{75}{7}p+\frac{50}{7} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-18}{20}+p)(\frac{-20}{20}+b)& =(\color{red}{p}+\color{orange}{\frac{-9}{10}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bp-1p-\frac{9}{10}b+\frac{9}{10}.1& \text{Uitwerken } \\ & =bp-1p-\frac{9}{10}b+\frac{9}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-20}{9}+q)(\frac{6}{20}+b)& =(\color{red}{q}+\color{orange}{\frac{-20}{9}}).(\color{green}{b}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-20}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{10}q-\frac{20}{9}b-\frac{20}{9}.\frac{3}{10}& \text{Uitwerken } \\ & =bq+\frac{3}{10}q-\frac{20}{9}b-\frac{60}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{3}{10}q-\frac{20}{9}b-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-17}{4})(\frac{-19}{20}+p)& =(\color{red}{p}+\color{orange}{\frac{17}{4}}).(\color{green}{p}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{17}{4})} . \color{green}{(p)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{19}{20}p+\frac{17}{4}p-\frac{17}{4}.\frac{19}{20}& \text{Uitwerken } \\ & =p^2+((\frac{-19}{20})+\frac{17}{4})p-(\frac{-323}{80}) & \text{Neem samen} \\ &=p^2+\frac{66}{20}p-(\frac{-323}{80}) & \text{Maak de som} \\ &=p^2+\frac{33}{10}p+\frac{323}{80} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{15}+p)(\frac{-4}{4}+b)& =(\color{red}{p}+\color{orange}{\frac{-3}{5}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bp-1p-\frac{3}{5}b+\frac{3}{5}.1& \text{Uitwerken } \\ & =bp-1p-\frac{3}{5}b+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{20}{10})(\frac{8}{10}+x)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{5}q-2x-2.\frac{4}{5}& \text{Uitwerken } \\ & =qx+\frac{4}{5}q-2x-\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+13)(a-\frac{-19}{6})& =(\color{red}{a}+\color{orange}{13}).(\color{green}{a}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(13)} . \color{green}{(a)} + \color{orange}{(13)} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{19}{6}a+13a+13.\frac{19}{6}& \text{Uitwerken } \\ & =a^2+(\frac{19}{6}+13)a+\frac{247}{6} & \text{Neem samen} \\ &=a^2+\frac{97}{6}a+\frac{247}{6} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-16}{8}+x)(\frac{-8}{16}-p)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{2}x+2p+2.\frac{1}{2}& \text{Uitwerken } \\ & =-px-\frac{1}{2}x+2p+\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{1}{2}x+2p+1 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-13)(a+\frac{-18}{8})& =(\color{red}{q}+\color{orange}{(-13)}).(\color{green}{a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(-13)} . \color{green}{(a)} + \color{orange}{(-13)} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{9}{4}q-13a+13.\frac{9}{4}& \text{Uitwerken } \\ & =aq-\frac{9}{4}q-13a+\frac{117}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{11}{14})(\frac{3}{12}-q)& =(\color{red}{b}+\color{orange}{\frac{-11}{14}}).(\color{green}{-q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{4}b+\frac{11}{14}q-\frac{11}{14}.\frac{1}{4}& \text{Uitwerken } \\ & =-bq+\frac{1}{4}b+\frac{11}{14}q-\frac{11}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{1}{7}-a)(x-\frac{-17}{14})& =(\color{red}{-a}+\color{orange}{\frac{1}{7}}).(\color{green}{x}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{1}{7})} . \color{green}{(x)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{17}{14}a+\frac{1}{7}x+\frac{1}{7}.\frac{17}{14}& \text{Uitwerken } \\ & =-ax-\frac{17}{14}a+\frac{1}{7}x+\frac{17}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-12 14:21:52
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