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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{6}{2})(\frac{-14}{13}-a)& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{-a}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(-3)} . \color{green}{(-a)} + \color{orange}{(-3)} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{14}{13}b+3a+3.\frac{14}{13}& \text{Uitwerken } \\ & =-ab-\frac{14}{13}b+3a+\frac{42}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{5}{18})(q-\frac{-20}{18})& =(\color{red}{a}+\color{orange}{\frac{-5}{18}}).(\color{green}{q}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{9}a-\frac{5}{18}q-\frac{5}{18}.\frac{10}{9}& \text{Uitwerken } \\ & =aq+\frac{10}{9}a-\frac{5}{18}q-\frac{50}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{10}{9}a-\frac{5}{18}q-\frac{25}{81} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-19}{17}-a)(\frac{-8}{17}-x)& =(\color{red}{-a}+\color{orange}{\frac{-19}{17}}).(\color{green}{-x}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{-19}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{8}{17}a+\frac{19}{17}x+\frac{19}{17}.\frac{8}{17}& \text{Uitwerken } \\ & =ax+\frac{8}{17}a+\frac{19}{17}x+\frac{152}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-20}{17}-p)(b-\frac{19}{10})& =(\color{red}{-p}+\color{orange}{\frac{-20}{17}}).(\color{green}{b}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{19}{10}p-\frac{20}{17}b+\frac{20}{17}.\frac{19}{10}& \text{Uitwerken } \\ & =-bp+\frac{19}{10}p-\frac{20}{17}b+\frac{380}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{19}{10}p-\frac{20}{17}b+\frac{38}{17} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-4}{9}-a)(\frac{-3}{3}-a)& =(\color{red}{-a}+\color{orange}{\frac{-4}{9}}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-4}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aa+1a+\frac{4}{9}a+\frac{4}{9}.1& \text{Uitwerken } \\ & =a^2+(1+\frac{4}{9})a+\frac{4}{9} & \text{Neem samen} \\ &=a^2+\frac{13}{9}a+\frac{4}{9} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-12}{18}-x)(\frac{-3}{14}-b)& =(\color{red}{-x}+\color{orange}{\frac{-2}{3}}).(\color{green}{-b}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{14}x+\frac{2}{3}b+\frac{2}{3}.\frac{3}{14}& \text{Uitwerken } \\ & =bx+\frac{3}{14}x+\frac{2}{3}b+\frac{6}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{14}x+\frac{2}{3}b+\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{5}+a)(\frac{4}{5}-a)& =(\color{red}{a}+\color{orange}{\frac{8}{5}}).(\color{green}{-a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{8}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{4}{5}a-\frac{8}{5}a+\frac{8}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =-a^2+(\frac{4}{5}+(\frac{-8}{5}))a+(\frac{-32}{25}) & \text{Neem samen} \\ &=-a^2-\frac{4}{5}a+(\frac{-32}{25}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(x-\frac{11}{14})(\frac{-8}{4}+b)& =(\color{red}{x}+\color{orange}{\frac{-11}{14}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-11}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bx-2x-\frac{11}{14}b+\frac{11}{14}.2& \text{Uitwerken } \\ & =bx-2x-\frac{11}{14}b+\frac{22}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-2x-\frac{11}{14}b+\frac{11}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a+\frac{13}{20})(\frac{8}{6}-x)& =(\color{red}{a}+\color{orange}{\frac{13}{20}}).(\color{green}{-x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{13}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{4}{3}a-\frac{13}{20}x+\frac{13}{20}.\frac{4}{3}& \text{Uitwerken } \\ & =-ax+\frac{4}{3}a-\frac{13}{20}x+\frac{52}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{4}{3}a-\frac{13}{20}x+\frac{13}{15} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-4}{11}-b)((-20)+x)& =(\color{red}{-b}+\color{orange}{\frac{-4}{11}}).(\color{green}{x}+\color{blue}{(-20)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(-20)} + \color{orange}{(\frac{-4}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = -bx+20b-\frac{4}{11}x+\frac{4}{11}.20& \text{Uitwerken } \\ & =-bx+20b-\frac{4}{11}x+\frac{80}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-4}{15})(p-\frac{-19}{12})& =(\color{red}{p}+\color{orange}{\frac{4}{15}}).(\color{green}{p}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{4}{15})} . \color{green}{(p)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{19}{12}p+\frac{4}{15}p+\frac{4}{15}.\frac{19}{12}& \text{Uitwerken } \\ & =p^2+(\frac{19}{12}+\frac{4}{15})p+\frac{76}{180} & \text{Neem samen} \\ &=p^2+\frac{111}{60}p+\frac{76}{180} & \text{Maak de som} \\ &=p^2+\frac{37}{20}p+\frac{19}{45} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-19}{12})(\frac{-14}{10}+a)& =(\color{red}{b}+\color{orange}{\frac{19}{12}}).(\color{green}{a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{19}{12})} . \color{green}{(a)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{5}b+\frac{19}{12}a-\frac{19}{12}.\frac{7}{5}& \text{Uitwerken } \\ & =ab-\frac{7}{5}b+\frac{19}{12}a-\frac{133}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-17 17:11:57
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