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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-18}{10})(q+\frac{-1}{7})& =(\color{red}{b}+\color{orange}{\frac{-9}{5}}).(\color{green}{q}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{7}b-\frac{9}{5}q+\frac{9}{5}.\frac{1}{7}& \text{Uitwerken } \\ & =bq-\frac{1}{7}b-\frac{9}{5}q+\frac{9}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-18}{12}-p)(\frac{-6}{16}-a)& =(\color{red}{-p}+\color{orange}{\frac{-3}{2}}).(\color{green}{-a}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{8}p+\frac{3}{2}a+\frac{3}{2}.\frac{3}{8}& \text{Uitwerken } \\ & =ap+\frac{3}{8}p+\frac{3}{2}a+\frac{9}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{14}{19})(\frac{5}{9}+b)& =(\color{red}{a}+\color{orange}{\frac{-14}{19}}).(\color{green}{b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{9}a-\frac{14}{19}b-\frac{14}{19}.\frac{5}{9}& \text{Uitwerken } \\ & =ab+\frac{5}{9}a-\frac{14}{19}b-\frac{70}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{16}{17}+q)(\frac{-9}{2}+q)& =(\color{red}{q}+\color{orange}{\frac{16}{17}}).(\color{green}{q}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{16}{17})} . \color{green}{(q)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{9}{2}q+\frac{16}{17}q-\frac{16}{17}.\frac{9}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-9}{2})+\frac{16}{17})q-(\frac{-144}{34}) & \text{Neem samen} \\ &=q^2-\frac{121}{34}q-(\frac{-144}{34}) & \text{Maak de som} \\ &=q^2-\frac{121}{34}q+\frac{72}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(x+\frac{4}{17})(\frac{-3}{12}-a)& =(\color{red}{x}+\color{orange}{\frac{4}{17}}).(\color{green}{-a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{4}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{4}{17})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{4}x-\frac{4}{17}a-\frac{4}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =-ax-\frac{1}{4}x-\frac{4}{17}a-\frac{4}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{1}{4}x-\frac{4}{17}a-\frac{1}{17} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{5}{14}+b)(\frac{-3}{7}-x)& =(\color{red}{b}+\color{orange}{\frac{5}{14}}).(\color{green}{-x}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{5}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{7}b-\frac{5}{14}x-\frac{5}{14}.\frac{3}{7}& \text{Uitwerken } \\ & =-bx-\frac{3}{7}b-\frac{5}{14}x-\frac{15}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{14}{14})(\frac{-12}{20}-p)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{5}q+1p+1.\frac{3}{5}& \text{Uitwerken } \\ & =-pq-\frac{3}{5}q+1p+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-18}{4}-b)(\frac{2}{10}-a)& =(\color{red}{-b}+\color{orange}{\frac{-9}{2}}).(\color{green}{-a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{5}b+\frac{9}{2}a-\frac{9}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =ab-\frac{1}{5}b+\frac{9}{2}a-\frac{9}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-9}{10}-p)(b-\frac{-1}{5})& =(\color{red}{-p}+\color{orange}{\frac{-9}{10}}).(\color{green}{b}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{5}p-\frac{9}{10}b-\frac{9}{10}.\frac{1}{5}& \text{Uitwerken } \\ & =-bp-\frac{1}{5}p-\frac{9}{10}b-\frac{9}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-6}{4}+b)(\frac{-5}{15}-q)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{-q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{3}b+\frac{3}{2}q+\frac{3}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =-bq-\frac{1}{3}b+\frac{3}{2}q+\frac{3}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{3}b+\frac{3}{2}q+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a+\frac{5}{20})(\frac{-20}{3}-a)& =(\color{red}{a}+\color{orange}{\frac{1}{4}}).(\color{green}{-a}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{20}{3}a-\frac{1}{4}a-\frac{1}{4}.\frac{20}{3}& \text{Uitwerken } \\ & =-a^2+((\frac{-20}{3})+(\frac{-1}{4}))a-\frac{20}{12} & \text{Neem samen} \\ &=-a^2-\frac{83}{12}a-\frac{20}{12} & \text{Maak de som} \\ &=-a^2-\frac{83}{12}a-\frac{5}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{14}{4}-q)(\frac{-15}{20}+b)& =(\color{red}{-q}+\color{orange}{\frac{7}{2}}).(\color{green}{b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{4}q+\frac{7}{2}b-\frac{7}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =-bq+\frac{3}{4}q+\frac{7}{2}b-\frac{21}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-04 07:14:35
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