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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-10}{10})(x+\frac{17}{18})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{18}q+1x+1.\frac{17}{18}& \text{Uitwerken } \\ & =qx+\frac{17}{18}q+1x+\frac{17}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{11}{12})(\frac{11}{17}-q)& =(\color{red}{x}+\color{orange}{\frac{-11}{12}}).(\color{green}{-q}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(-q)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{11}{17}x+\frac{11}{12}q-\frac{11}{12}.\frac{11}{17}& \text{Uitwerken } \\ & =-qx+\frac{11}{17}x+\frac{11}{12}q-\frac{121}{204} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-20}{4}+a)(\frac{-15}{9}-q)& =(\color{red}{a}+\color{orange}{(-5)}).(\color{green}{-q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(-5)} . \color{green}{(-q)} + \color{orange}{(-5)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{3}a+5q+5.\frac{5}{3}& \text{Uitwerken } \\ & =-aq-\frac{5}{3}a+5q+\frac{25}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{13}{13}+p)(q-\frac{-4}{14})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{7}p+1q+1.\frac{2}{7}& \text{Uitwerken } \\ & =pq+\frac{2}{7}p+1q+\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-18}{20})(q-\frac{15}{4})& =(\color{red}{p}+\color{orange}{\frac{9}{10}}).(\color{green}{q}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{9}{10})} . \color{green}{(q)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{15}{4}p+\frac{9}{10}q-\frac{9}{10}.\frac{15}{4}& \text{Uitwerken } \\ & =pq-\frac{15}{4}p+\frac{9}{10}q-\frac{135}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{15}{4}p+\frac{9}{10}q-\frac{27}{8} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-16}{5})(q+\frac{15}{10})& =(\color{red}{p}+\color{orange}{\frac{16}{5}}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{16}{5})} . \color{green}{(q)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{2}p+\frac{16}{5}q+\frac{16}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =pq+\frac{3}{2}p+\frac{16}{5}q+\frac{48}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{3}{2}p+\frac{16}{5}q+\frac{24}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{13}-b)(a+\frac{11}{15})& =(\color{red}{-b}+\color{orange}{\frac{8}{13}}).(\color{green}{a}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{8}{13})} . \color{green}{(a)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{11}{15}b+\frac{8}{13}a+\frac{8}{13}.\frac{11}{15}& \text{Uitwerken } \\ & =-ab-\frac{11}{15}b+\frac{8}{13}a+\frac{88}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-12}{11}+b)(q+\frac{13}{18})& =(\color{red}{b}+\color{orange}{\frac{-12}{11}}).(\color{green}{q}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{18}b-\frac{12}{11}q-\frac{12}{11}.\frac{13}{18}& \text{Uitwerken } \\ & =bq+\frac{13}{18}b-\frac{12}{11}q-\frac{156}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{13}{18}b-\frac{12}{11}q-\frac{26}{33} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-16}{15})(\frac{-9}{11}-x)& =(\color{red}{b}+\color{orange}{\frac{16}{15}}).(\color{green}{-x}+\color{blue}{\frac{-9}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{11})} + \color{orange}{(\frac{16}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(\frac{-9}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{9}{11}b-\frac{16}{15}x-\frac{16}{15}.\frac{9}{11}& \text{Uitwerken } \\ & =-bx-\frac{9}{11}b-\frac{16}{15}x-\frac{144}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{9}{11}b-\frac{16}{15}x-\frac{48}{55} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-1}{4}-b)(q+\frac{11}{5})& =(\color{red}{-b}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{11}{5}b-\frac{1}{4}q-\frac{1}{4}.\frac{11}{5}& \text{Uitwerken } \\ & =-bq-\frac{11}{5}b-\frac{1}{4}q-\frac{11}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{6}+b)(\frac{-7}{12}-b)& =(\color{red}{b}+\color{orange}{\frac{-7}{3}}).(\color{green}{-b}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{7}{12}b+\frac{7}{3}b+\frac{7}{3}.\frac{7}{12}& \text{Uitwerken } \\ & =-b^2+((\frac{-7}{12})+\frac{7}{3})b+(\frac{-49}{36}) & \text{Neem samen} \\ &=-b^2+\frac{21}{12}b+(\frac{-49}{36}) & \text{Maak de som} \\ &=-b^2+\frac{7}{4}b+(\frac{-49}{36}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{-3}{3}+q)(\frac{12}{3}-x)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(4)} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -qx+4q+1x-1.4& \text{Uitwerken } \\ & =-qx+4q+1x-4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-05 06:56:29
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