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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{6}{9}+p)(q-\frac{-6}{5})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{6}{5}p+\frac{2}{3}q+\frac{2}{3}.\frac{6}{5}& \text{Uitwerken } \\ & =pq+\frac{6}{5}p+\frac{2}{3}q+\frac{12}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{6}{5}p+\frac{2}{3}q+\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{9}{10}+b)(\frac{-15}{4}+a)& =(\color{red}{b}+\color{orange}{\frac{9}{10}}).(\color{green}{a}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{9}{10})} . \color{green}{(a)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{4}b+\frac{9}{10}a-\frac{9}{10}.\frac{15}{4}& \text{Uitwerken } \\ & =ab-\frac{15}{4}b+\frac{9}{10}a-\frac{135}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{15}{4}b+\frac{9}{10}a-\frac{27}{8} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{15}+q)(\frac{-19}{14}-a)& =(\color{red}{q}+\color{orange}{\frac{-14}{15}}).(\color{green}{-a}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{-14}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{14}q+\frac{14}{15}a+\frac{14}{15}.\frac{19}{14}& \text{Uitwerken } \\ & =-aq-\frac{19}{14}q+\frac{14}{15}a+\frac{266}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{19}{14}q+\frac{14}{15}a+\frac{19}{15} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{7}{19}+a)(q+\frac{6}{3})& =(\color{red}{a}+\color{orange}{\frac{7}{19}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{7}{19})} . \color{green}{(q)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq+2a+\frac{7}{19}q+\frac{7}{19}.2& \text{Uitwerken } \\ & =aq+2a+\frac{7}{19}q+\frac{14}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{14}{2}+q)(p-\frac{10}{4})& =(\color{red}{q}+\color{orange}{7}).(\color{green}{p}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(7)} . \color{green}{(p)} + \color{orange}{(7)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{2}q+7p-7.\frac{5}{2}& \text{Uitwerken } \\ & =pq-\frac{5}{2}q+7p-\frac{35}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-20}{15})(p-\frac{-13}{10})& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{10}b-\frac{4}{3}p-\frac{4}{3}.\frac{13}{10}& \text{Uitwerken } \\ & =bp+\frac{13}{10}b-\frac{4}{3}p-\frac{52}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{13}{10}b-\frac{4}{3}p-\frac{26}{15} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a+\frac{19}{10})(\frac{9}{15}-x)& =(\color{red}{a}+\color{orange}{\frac{19}{10}}).(\color{green}{-x}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{19}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{5}a-\frac{19}{10}x+\frac{19}{10}.\frac{3}{5}& \text{Uitwerken } \\ & =-ax+\frac{3}{5}a-\frac{19}{10}x+\frac{57}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{9}{13}-b)(q-\frac{-19}{5})& =(\color{red}{-b}+\color{orange}{\frac{9}{13}}).(\color{green}{q}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{9}{13})} . \color{green}{(q)} + \color{orange}{(\frac{9}{13})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{19}{5}b+\frac{9}{13}q+\frac{9}{13}.\frac{19}{5}& \text{Uitwerken } \\ & =-bq-\frac{19}{5}b+\frac{9}{13}q+\frac{171}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+12)(\frac{-8}{18}+p)& =(\color{red}{x}+\color{orange}{12}).(\color{green}{p}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(12)} . \color{green}{(p)} + \color{orange}{(12)} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{9}x+12p-12.\frac{4}{9}& \text{Uitwerken } \\ & =px-\frac{4}{9}x+12p-\frac{48}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{4}{9}x+12p-\frac{16}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b+\frac{9}{13})(18-b)& =(\color{red}{b}+\color{orange}{\frac{9}{13}}).(\color{green}{-b}+\color{blue}{18})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(18)} + \color{orange}{(\frac{9}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{13})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = -bb+18b-\frac{9}{13}b+\frac{9}{13}.18& \text{Uitwerken } \\ & =-b^2+(18+(\frac{-9}{13}))b+(\frac{-162}{13}) & \text{Neem samen} \\ &=-b^2+\frac{225}{13}b+(\frac{-162}{13}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{3}{14}-p)(\frac{-19}{19}+x)& =(\color{red}{-p}+\color{orange}{\frac{3}{14}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(\frac{3}{14})} . \color{green}{(x)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -px+1p+\frac{3}{14}x-\frac{3}{14}.1& \text{Uitwerken } \\ & =-px+1p+\frac{3}{14}x-\frac{3}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{15}{9})(\frac{7}{18}+a)& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{a}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{18}p-\frac{5}{3}a-\frac{5}{3}.\frac{7}{18}& \text{Uitwerken } \\ & =ap+\frac{7}{18}p-\frac{5}{3}a-\frac{35}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-11-29 17:57:34
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