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

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Werk uit en vereenvoudig

  1. \((\frac{-17}{16}-a)(p+\frac{-19}{6})\)
  2. \((x+\frac{5}{7})(q-\frac{-12}{2})\)
  3. \((\frac{-17}{19}-q)(\frac{8}{6}-q)\)
  4. \((x-\frac{-19}{3})(\frac{12}{12}-b)\)
  5. \((q+7)(\frac{15}{13}+p)\)
  6. \((b+\frac{17}{10})(\frac{-14}{2}-x)\)
  7. \((\frac{-20}{10}-p)(\frac{19}{14}+q)\)
  8. \((b-\frac{19}{11})(\frac{3}{18}-a)\)
  9. \((\frac{-10}{12}+q)(q-\frac{-10}{20})\)
  10. \((18-a)(x-\frac{20}{19})\)
  11. \((q+\frac{13}{13})(x+\frac{-12}{8})\)
  12. \((\frac{12}{2}-x)(\frac{10}{10}-a)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-17}{16}-a)(p+\frac{-19}{6})& =(\color{red}{-a}+\color{orange}{\frac{-17}{16}}).(\color{green}{p}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{6}a-\frac{17}{16}p+\frac{17}{16}.\frac{19}{6}& \text{Uitwerken } \\ & =-ap+\frac{19}{6}a-\frac{17}{16}p+\frac{323}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{5}{7})(q-\frac{-12}{2})& =(\color{red}{x}+\color{orange}{\frac{5}{7}}).(\color{green}{q}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(6)} + \color{orange}{(\frac{5}{7})} . \color{green}{(q)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = qx+6x+\frac{5}{7}q+\frac{5}{7}.6& \text{Uitwerken } \\ & =qx+6x+\frac{5}{7}q+\frac{30}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-17}{19}-q)(\frac{8}{6}-q)& =(\color{red}{-q}+\color{orange}{\frac{-17}{19}}).(\color{green}{-q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{4}{3}q+\frac{17}{19}q-\frac{17}{19}.\frac{4}{3}& \text{Uitwerken } \\ & =q^2+((\frac{-4}{3})+\frac{17}{19})q-(\frac{-68}{57}) & \text{Neem samen} \\ &=q^2-\frac{25}{57}q-(\frac{-68}{57}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-19}{3})(\frac{12}{12}-b)& =(\color{red}{x}+\color{orange}{\frac{19}{3}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{19}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1x-\frac{19}{3}b+\frac{19}{3}.1& \text{Uitwerken } \\ & =-bx+1x-\frac{19}{3}b+\frac{19}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+7)(\frac{15}{13}+p)& =(\color{red}{q}+\color{orange}{7}).(\color{green}{p}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(7)} . \color{green}{(p)} + \color{orange}{(7)} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{15}{13}q+7p+7.\frac{15}{13}& \text{Uitwerken } \\ & =pq+\frac{15}{13}q+7p+\frac{105}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{17}{10})(\frac{-14}{2}-x)& =(\color{red}{b}+\color{orange}{\frac{17}{10}}).(\color{green}{-x}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(-7)} + \color{orange}{(\frac{17}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = -bx-7b-\frac{17}{10}x-\frac{17}{10}.7& \text{Uitwerken } \\ & =-bx-7b-\frac{17}{10}x-\frac{119}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-20}{10}-p)(\frac{19}{14}+q)& =(\color{red}{-p}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{14}p-2q-2.\frac{19}{14}& \text{Uitwerken } \\ & =-pq-\frac{19}{14}p-2q-\frac{38}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{19}{14}p-2q-\frac{19}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b-\frac{19}{11})(\frac{3}{18}-a)& =(\color{red}{b}+\color{orange}{\frac{-19}{11}}).(\color{green}{-a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{6}b+\frac{19}{11}a-\frac{19}{11}.\frac{1}{6}& \text{Uitwerken } \\ & =-ab+\frac{1}{6}b+\frac{19}{11}a-\frac{19}{66} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-10}{12}+q)(q-\frac{-10}{20})& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{2}q-\frac{5}{6}q-\frac{5}{6}.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+(\frac{1}{2}+(\frac{-5}{6}))q-(\frac{-5}{12}) & \text{Neem samen} \\ &=q^2-\frac{2}{6}q-(\frac{-5}{12}) & \text{Maak de som} \\ &=q^2-\frac{1}{3}q+\frac{5}{12} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(18-a)(x-\frac{20}{19})& =(\color{red}{-a}+\color{orange}{18}).(\color{green}{x}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(18)} . \color{green}{(x)} + \color{orange}{(18)} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{20}{19}a+18x-18.\frac{20}{19}& \text{Uitwerken } \\ & =-ax+\frac{20}{19}a+18x-\frac{360}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{13}{13})(x+\frac{-12}{8})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{2}q+1x-1.\frac{3}{2}& \text{Uitwerken } \\ & =qx-\frac{3}{2}q+1x-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{12}{2}-x)(\frac{10}{10}-a)& =(\color{red}{-x}+\color{orange}{6}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(6)} . \color{green}{(-a)} + \color{orange}{(6)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x-6a+6.1& \text{Uitwerken } \\ & =ax-1x-6a+6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-31 23:33:10
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