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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-6}{4}-b)(\frac{-18}{17}+q)& =(\color{red}{-b}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{18}{17}b-\frac{3}{2}q+\frac{3}{2}.\frac{18}{17}& \text{Uitwerken } \\ & =-bq+\frac{18}{17}b-\frac{3}{2}q+\frac{54}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{18}{17}b-\frac{3}{2}q+\frac{27}{17} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{9}+x)(q+\frac{-2}{19})& =(\color{red}{x}+\color{orange}{\frac{19}{9}}).(\color{green}{q}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{19}{9})} . \color{green}{(q)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{19}x+\frac{19}{9}q-\frac{19}{9}.\frac{2}{19}& \text{Uitwerken } \\ & =qx-\frac{2}{19}x+\frac{19}{9}q-\frac{38}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{2}{19}x+\frac{19}{9}q-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-17}{20}+b)(\frac{-16}{18}+p)& =(\color{red}{b}+\color{orange}{\frac{-17}{20}}).(\color{green}{p}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{9}b-\frac{17}{20}p+\frac{17}{20}.\frac{8}{9}& \text{Uitwerken } \\ & =bp-\frac{8}{9}b-\frac{17}{20}p+\frac{136}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{8}{9}b-\frac{17}{20}p+\frac{34}{45} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a+\frac{14}{17})(p-\frac{3}{14})& =(\color{red}{a}+\color{orange}{\frac{14}{17}}).(\color{green}{p}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{14}{17})} . \color{green}{(p)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{14}a+\frac{14}{17}p-\frac{14}{17}.\frac{3}{14}& \text{Uitwerken } \\ & =ap-\frac{3}{14}a+\frac{14}{17}p-\frac{42}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{3}{14}a+\frac{14}{17}p-\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{12}+a)(p+\frac{-17}{12})& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{17}{12}a+\frac{1}{3}p-\frac{1}{3}.\frac{17}{12}& \text{Uitwerken } \\ & =ap-\frac{17}{12}a+\frac{1}{3}p-\frac{17}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-4}{8}-x)(\frac{2}{17}+q)& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{17}x-\frac{1}{2}q-\frac{1}{2}.\frac{2}{17}& \text{Uitwerken } \\ & =-qx-\frac{2}{17}x-\frac{1}{2}q-\frac{2}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{2}{17}x-\frac{1}{2}q-\frac{1}{17} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{2}-p)(p-\frac{2}{11})& =(\color{red}{-p}+\color{orange}{\frac{-9}{2}}).(\color{green}{p}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{2}{11}p-\frac{9}{2}p+\frac{9}{2}.\frac{2}{11}& \text{Uitwerken } \\ & =-p^2+(\frac{2}{11}+(\frac{-9}{2}))p+(\frac{-18}{22}) & \text{Neem samen} \\ &=-p^2-\frac{95}{22}p+(\frac{-18}{22}) & \text{Maak de som} \\ &=-p^2-\frac{95}{22}p+(\frac{-9}{11}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(a-\frac{19}{20})(\frac{17}{7}+p)& =(\color{red}{a}+\color{orange}{\frac{-19}{20}}).(\color{green}{p}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{7}a-\frac{19}{20}p-\frac{19}{20}.\frac{17}{7}& \text{Uitwerken } \\ & =ap+\frac{17}{7}a-\frac{19}{20}p-\frac{323}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{8}{5})(\frac{-7}{11}+q)& =(\color{red}{q}+\color{orange}{\frac{-8}{5}}).(\color{green}{q}+\color{blue}{\frac{-7}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{11})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-7}{11})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{11}q-\frac{8}{5}q+\frac{8}{5}.\frac{7}{11}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{11})+(\frac{-8}{5}))q+\frac{56}{55} & \text{Neem samen} \\ &=q^2-\frac{123}{55}q+\frac{56}{55} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{6}{9}-q)(\frac{13}{6}+p)& =(\color{red}{-q}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{13}{6}q+\frac{2}{3}p+\frac{2}{3}.\frac{13}{6}& \text{Uitwerken } \\ & =-pq-\frac{13}{6}q+\frac{2}{3}p+\frac{26}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{13}{6}q+\frac{2}{3}p+\frac{13}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{14}-b)(p+\frac{9}{9})& =(\color{red}{-b}+\color{orange}{\frac{-19}{14}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1b-\frac{19}{14}p-\frac{19}{14}.1& \text{Uitwerken } \\ & =-bp-1b-\frac{19}{14}p-\frac{19}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-5}{2})(\frac{8}{20}-q)& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{-q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{5}b+\frac{5}{2}q-\frac{5}{2}.\frac{2}{5}& \text{Uitwerken } \\ & =-bq+\frac{2}{5}b+\frac{5}{2}q-\frac{10}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{2}{5}b+\frac{5}{2}q-1 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-12 20:15:23
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