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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-11}{10})(b+\frac{-8}{2})& =(\color{red}{q}+\color{orange}{\frac{-11}{10}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(\frac{-11}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bq-4q-\frac{11}{10}b+\frac{11}{10}.4& \text{Uitwerken } \\ & =bq-4q-\frac{11}{10}b+\frac{44}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-4q-\frac{11}{10}b+\frac{22}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{17}{20}-p)(b-\frac{-8}{10})& =(\color{red}{-p}+\color{orange}{\frac{17}{20}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{17}{20})} . \color{green}{(b)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{5}p+\frac{17}{20}b+\frac{17}{20}.\frac{4}{5}& \text{Uitwerken } \\ & =-bp-\frac{4}{5}p+\frac{17}{20}b+\frac{68}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{4}{5}p+\frac{17}{20}b+\frac{17}{25} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-11}{7})(19-p)& =(\color{red}{x}+\color{orange}{\frac{11}{7}}).(\color{green}{-p}+\color{blue}{19})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(19)} + \color{orange}{(\frac{11}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = -px+19x-\frac{11}{7}p+\frac{11}{7}.19& \text{Uitwerken } \\ & =-px+19x-\frac{11}{7}p+\frac{209}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-3}{2})(\frac{-19}{13}+p)& =(\color{red}{p}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{19}{13}p-\frac{3}{2}p+\frac{3}{2}.\frac{19}{13}& \text{Uitwerken } \\ & =p^2+((\frac{-19}{13})+(\frac{-3}{2}))p+\frac{57}{26} & \text{Neem samen} \\ &=p^2-\frac{77}{26}p+\frac{57}{26} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a+\frac{13}{20})(\frac{-18}{18}+a)& =(\color{red}{a}+\color{orange}{\frac{13}{20}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{13}{20})} . \color{green}{(a)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aa-1a+\frac{13}{20}a-\frac{13}{20}.1& \text{Uitwerken } \\ & =a^2+((-1)+\frac{13}{20})a-(\frac{-13}{20}) & \text{Neem samen} \\ &=a^2-\frac{7}{20}a-(\frac{-13}{20}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(p-\frac{9}{15})(\frac{12}{17}-x)& =(\color{red}{p}+\color{orange}{\frac{-3}{5}}).(\color{green}{-x}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{12}{17}p+\frac{3}{5}x-\frac{3}{5}.\frac{12}{17}& \text{Uitwerken } \\ & =-px+\frac{12}{17}p+\frac{3}{5}x-\frac{36}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{19}{6}-a)(\frac{-2}{11}-p)& =(\color{red}{-a}+\color{orange}{\frac{19}{6}}).(\color{green}{-p}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{19}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{6})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{11}a-\frac{19}{6}p-\frac{19}{6}.\frac{2}{11}& \text{Uitwerken } \\ & =ap+\frac{2}{11}a-\frac{19}{6}p-\frac{38}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{2}{11}a-\frac{19}{6}p-\frac{19}{33} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{3}{2})(b+\frac{-19}{5})& =(\color{red}{x}+\color{orange}{\frac{-3}{2}}).(\color{green}{b}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{5}x-\frac{3}{2}b+\frac{3}{2}.\frac{19}{5}& \text{Uitwerken } \\ & =bx-\frac{19}{5}x-\frac{3}{2}b+\frac{57}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-11}{8}+p)(\frac{-4}{6}+b)& =(\color{red}{p}+\color{orange}{\frac{-11}{8}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{3}p-\frac{11}{8}b+\frac{11}{8}.\frac{2}{3}& \text{Uitwerken } \\ & =bp-\frac{2}{3}p-\frac{11}{8}b+\frac{22}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{2}{3}p-\frac{11}{8}b+\frac{11}{12} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{8}{6}+p)(\frac{-4}{3}+a)& =(\color{red}{p}+\color{orange}{\frac{4}{3}}).(\color{green}{a}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{4}{3}p+\frac{4}{3}a-\frac{4}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =ap-\frac{4}{3}p+\frac{4}{3}a-\frac{16}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{20}{11})(\frac{14}{8}+x)& =(\color{red}{x}+\color{orange}{\frac{20}{11}}).(\color{green}{x}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{20}{11})} . \color{green}{(x)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{7}{4}x+\frac{20}{11}x+\frac{20}{11}.\frac{7}{4}& \text{Uitwerken } \\ & =x^2+(\frac{7}{4}+\frac{20}{11})x+\frac{140}{44} & \text{Neem samen} \\ &=x^2+\frac{157}{44}x+\frac{140}{44} & \text{Maak de som} \\ &=x^2+\frac{157}{44}x+\frac{35}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{20}{2}-q)(\frac{-3}{13}-q)& =(\color{red}{-q}+\color{orange}{10}).(\color{green}{-q}+\color{blue}{\frac{-3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{13})} + \color{orange}{(10)} . \color{green}{(-q)} + \color{orange}{(10)} . \color{blue}{(\frac{-3}{13})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{13}q-10q-10.\frac{3}{13}& \text{Uitwerken } \\ & =q^2+(\frac{3}{13}+(-10))q-(\frac{-30}{13}) & \text{Neem samen} \\ &=q^2-\frac{127}{13}q-(\frac{-30}{13}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-17 20:14:33
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