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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{18}{10})(\frac{-13}{6}-x)& =(\color{red}{q}+\color{orange}{\frac{9}{5}}).(\color{green}{-x}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{9}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{6}q-\frac{9}{5}x-\frac{9}{5}.\frac{13}{6}& \text{Uitwerken } \\ & =-qx-\frac{13}{6}q-\frac{9}{5}x-\frac{117}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{13}{6}q-\frac{9}{5}x-\frac{39}{10} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b-\frac{18}{17})(a+\frac{-11}{14})& =(\color{red}{b}+\color{orange}{\frac{-18}{17}}).(\color{green}{a}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{14}b-\frac{18}{17}a+\frac{18}{17}.\frac{11}{14}& \text{Uitwerken } \\ & =ab-\frac{11}{14}b-\frac{18}{17}a+\frac{198}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{11}{14}b-\frac{18}{17}a+\frac{99}{119} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{19}{20})(a-\frac{-9}{13})& =(\color{red}{q}+\color{orange}{\frac{19}{20}}).(\color{green}{a}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{19}{20})} . \color{green}{(a)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{13}q+\frac{19}{20}a+\frac{19}{20}.\frac{9}{13}& \text{Uitwerken } \\ & =aq+\frac{9}{13}q+\frac{19}{20}a+\frac{171}{260} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{13}{13})(q-\frac{1}{5})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{5}b-1q+1.\frac{1}{5}& \text{Uitwerken } \\ & =bq-\frac{1}{5}b-1q+\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{19}-p)(\frac{14}{17}+a)& =(\color{red}{-p}+\color{orange}{\frac{-10}{19}}).(\color{green}{a}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{14}{17}p-\frac{10}{19}a-\frac{10}{19}.\frac{14}{17}& \text{Uitwerken } \\ & =-ap-\frac{14}{17}p-\frac{10}{19}a-\frac{140}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-1}{18})(\frac{-19}{8}-p)& =(\color{red}{q}+\color{orange}{\frac{-1}{18}}).(\color{green}{-p}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{-1}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{8}q+\frac{1}{18}p+\frac{1}{18}.\frac{19}{8}& \text{Uitwerken } \\ & =-pq-\frac{19}{8}q+\frac{1}{18}p+\frac{19}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{-18}{17})(x+\frac{-2}{9})& =(\color{red}{p}+\color{orange}{\frac{-18}{17}}).(\color{green}{x}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{9}p-\frac{18}{17}x+\frac{18}{17}.\frac{2}{9}& \text{Uitwerken } \\ & =px-\frac{2}{9}p-\frac{18}{17}x+\frac{36}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{2}{9}p-\frac{18}{17}x+\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q+\frac{10}{14})(\frac{10}{7}-q)& =(\color{red}{q}+\color{orange}{\frac{5}{7}}).(\color{green}{-q}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{5}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{10}{7}q-\frac{5}{7}q+\frac{5}{7}.\frac{10}{7}& \text{Uitwerken } \\ & =-q^2+(\frac{10}{7}+(\frac{-5}{7}))q+(\frac{-50}{49}) & \text{Neem samen} \\ &=-q^2+\frac{5}{7}q+(\frac{-50}{49}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-16}{5})(p-\frac{-10}{16})& =(\color{red}{p}+\color{orange}{\frac{-16}{5}}).(\color{green}{p}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{8}p-\frac{16}{5}p-\frac{16}{5}.\frac{5}{8}& \text{Uitwerken } \\ & =p^2+(\frac{5}{8}+(\frac{-16}{5}))p-(\frac{-80}{40}) & \text{Neem samen} \\ &=p^2-\frac{103}{40}p-(\frac{-80}{40}) & \text{Maak de som} \\ &=p^2-\frac{103}{40}p+2 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(\frac{-14}{9}+p)(x-15)& =(\color{red}{p}+\color{orange}{\frac{-14}{9}}).(\color{green}{x}+\color{blue}{(-15)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-15)} + \color{orange}{(\frac{-14}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = px-15p-\frac{14}{9}x+\frac{14}{9}.15& \text{Uitwerken } \\ & =px-15p-\frac{14}{9}x+\frac{210}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-15p-\frac{14}{9}x+\frac{70}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{11}+b)(q+\frac{-9}{10})& =(\color{red}{b}+\color{orange}{\frac{14}{11}}).(\color{green}{q}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{14}{11})} . \color{green}{(q)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{9}{10}b+\frac{14}{11}q-\frac{14}{11}.\frac{9}{10}& \text{Uitwerken } \\ & =bq-\frac{9}{10}b+\frac{14}{11}q-\frac{126}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{9}{10}b+\frac{14}{11}q-\frac{63}{55} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-8}{12}-x)(\frac{-2}{6}+q)& =(\color{red}{-x}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{3}x-\frac{2}{3}q+\frac{2}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =-qx+\frac{1}{3}x-\frac{2}{3}q+\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-21 17:24:56
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