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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{16}{19}+b)(\frac{1}{8}-b)& =(\color{red}{b}+\color{orange}{\frac{16}{19}}).(\color{green}{-b}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{16}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{8}b-\frac{16}{19}b+\frac{16}{19}.\frac{1}{8}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{8}+(\frac{-16}{19}))b+(\frac{-16}{152}) & \text{Neem samen} \\ &=-b^2-\frac{109}{152}b+(\frac{-16}{152}) & \text{Maak de som} \\ &=-b^2-\frac{109}{152}b+(\frac{-2}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{19}+q)(\frac{18}{7}-q)& =(\color{red}{q}+\color{orange}{\frac{8}{19}}).(\color{green}{-q}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{8}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{18}{7}q-\frac{8}{19}q+\frac{8}{19}.\frac{18}{7}& \text{Uitwerken } \\ & =-q^2+(\frac{18}{7}+(\frac{-8}{19}))q+(\frac{-144}{133}) & \text{Neem samen} \\ &=-q^2+\frac{286}{133}q+(\frac{-144}{133}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-19}{13}-b)(x-\frac{-20}{4})& =(\color{red}{-b}+\color{orange}{\frac{-19}{13}}).(\color{green}{x}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(5)} + \color{orange}{(\frac{-19}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -bx-5b-\frac{19}{13}x-\frac{19}{13}.5& \text{Uitwerken } \\ & =-bx-5b-\frac{19}{13}x-\frac{95}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{19}{10}-x)(\frac{-6}{18}+x)& =(\color{red}{-x}+\color{orange}{\frac{19}{10}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{19}{10})} . \color{green}{(x)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{3}x+\frac{19}{10}x-\frac{19}{10}.\frac{1}{3}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{3}+\frac{19}{10})x-\frac{19}{30} & \text{Neem samen} \\ &=-x^2+\frac{67}{30}x-\frac{19}{30} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{12}{2}+p)(p-\frac{-18}{11})& =(\color{red}{p}+\color{orange}{6}).(\color{green}{p}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(6)} . \color{green}{(p)} + \color{orange}{(6)} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{18}{11}p+6p+6.\frac{18}{11}& \text{Uitwerken } \\ & =p^2+(\frac{18}{11}+6)p+\frac{108}{11} & \text{Neem samen} \\ &=p^2+\frac{84}{11}p+\frac{108}{11} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-2}{11})(\frac{-13}{6}+p)& =(\color{red}{b}+\color{orange}{\frac{-2}{11}}).(\color{green}{p}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{6}b-\frac{2}{11}p+\frac{2}{11}.\frac{13}{6}& \text{Uitwerken } \\ & =bp-\frac{13}{6}b-\frac{2}{11}p+\frac{26}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{13}{6}b-\frac{2}{11}p+\frac{13}{33} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{4}-q)(\frac{-17}{11}-a)& =(\color{red}{-q}+\color{orange}{\frac{9}{4}}).(\color{green}{-a}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(\frac{9}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{11}q-\frac{9}{4}a-\frac{9}{4}.\frac{17}{11}& \text{Uitwerken } \\ & =aq+\frac{17}{11}q-\frac{9}{4}a-\frac{153}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{10}{19})(a+\frac{17}{8})& =(\color{red}{p}+\color{orange}{\frac{10}{19}}).(\color{green}{a}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{10}{19})} . \color{green}{(a)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{8}p+\frac{10}{19}a+\frac{10}{19}.\frac{17}{8}& \text{Uitwerken } \\ & =ap+\frac{17}{8}p+\frac{10}{19}a+\frac{170}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{17}{8}p+\frac{10}{19}a+\frac{85}{76} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{3}{4}-q)(q-\frac{13}{3})& =(\color{red}{-q}+\color{orange}{\frac{3}{4}}).(\color{green}{q}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{13}{3}q+\frac{3}{4}q-\frac{3}{4}.\frac{13}{3}& \text{Uitwerken } \\ & =-q^2+(\frac{13}{3}+\frac{3}{4})q-\frac{39}{12} & \text{Neem samen} \\ &=-q^2+\frac{61}{12}q-\frac{39}{12} & \text{Maak de som} \\ &=-q^2+\frac{61}{12}q-\frac{13}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-19}{20}-p)(q-\frac{-3}{9})& =(\color{red}{-p}+\color{orange}{\frac{-19}{20}}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{3}p-\frac{19}{20}q-\frac{19}{20}.\frac{1}{3}& \text{Uitwerken } \\ & =-pq-\frac{1}{3}p-\frac{19}{20}q-\frac{19}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{17}{20}+q)(x-\frac{20}{20})& =(\color{red}{q}+\color{orange}{\frac{17}{20}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{17}{20})} . \color{green}{(x)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1q+\frac{17}{20}x-\frac{17}{20}.1& \text{Uitwerken } \\ & =qx-1q+\frac{17}{20}x-\frac{17}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-14}{8})(\frac{8}{12}-q)& =(\color{red}{b}+\color{orange}{\frac{7}{4}}).(\color{green}{-q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{7}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{3}b-\frac{7}{4}q+\frac{7}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =-bq+\frac{2}{3}b-\frac{7}{4}q+\frac{14}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{2}{3}b-\frac{7}{4}q+\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-20 15:19:26
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