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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-1}{6})(p-\frac{15}{17})& =(\color{red}{q}+\color{orange}{\frac{1}{6}}).(\color{green}{p}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{1}{6})} . \color{green}{(p)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{15}{17}q+\frac{1}{6}p-\frac{1}{6}.\frac{15}{17}& \text{Uitwerken } \\ & =pq-\frac{15}{17}q+\frac{1}{6}p-\frac{15}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{15}{17}q+\frac{1}{6}p-\frac{5}{34} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{18}{5})(\frac{4}{10}-b)& =(\color{red}{b}+\color{orange}{\frac{18}{5}}).(\color{green}{-b}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{18}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{2}{5}b-\frac{18}{5}b+\frac{18}{5}.\frac{2}{5}& \text{Uitwerken } \\ & =-b^2+(\frac{2}{5}+(\frac{-18}{5}))b+(\frac{-36}{25}) & \text{Neem samen} \\ &=-b^2-\frac{16}{5}b+(\frac{-36}{25}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}((-17)+q)(\frac{1}{14}-p)& =(\color{red}{q}+\color{orange}{(-17)}).(\color{green}{-p}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(-17)} . \color{green}{(-p)} + \color{orange}{(-17)} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{14}q+17p-17.\frac{1}{14}& \text{Uitwerken } \\ & =-pq+\frac{1}{14}q+17p-\frac{17}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-15}{4}-q)(\frac{-1}{10}-q)& =(\color{red}{-q}+\color{orange}{\frac{-15}{4}}).(\color{green}{-q}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{10}q+\frac{15}{4}q+\frac{15}{4}.\frac{1}{10}& \text{Uitwerken } \\ & =q^2+(\frac{1}{10}+\frac{15}{4})q+\frac{15}{40} & \text{Neem samen} \\ &=q^2+\frac{77}{20}q+\frac{15}{40} & \text{Maak de som} \\ &=q^2+\frac{77}{20}q+\frac{3}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{14}{2}+a)(b-\frac{-19}{9})& =(\color{red}{a}+\color{orange}{7}).(\color{green}{b}+\color{blue}{\frac{19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{19}{9})} + \color{orange}{(7)} . \color{green}{(b)} + \color{orange}{(7)} . \color{blue}{(\frac{19}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{9}a+7b+7.\frac{19}{9}& \text{Uitwerken } \\ & =ab+\frac{19}{9}a+7b+\frac{133}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-11}{9}-a)(x+\frac{18}{19})& =(\color{red}{-a}+\color{orange}{\frac{-11}{9}}).(\color{green}{x}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{18}{19}a-\frac{11}{9}x-\frac{11}{9}.\frac{18}{19}& \text{Uitwerken } \\ & =-ax-\frac{18}{19}a-\frac{11}{9}x-\frac{198}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{18}{19}a-\frac{11}{9}x-\frac{22}{19} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{14}{16})(p-\frac{-13}{20})& =(\color{red}{x}+\color{orange}{\frac{-7}{8}}).(\color{green}{p}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{20}x-\frac{7}{8}p-\frac{7}{8}.\frac{13}{20}& \text{Uitwerken } \\ & =px+\frac{13}{20}x-\frac{7}{8}p-\frac{91}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{13}{11}+q)(x+\frac{8}{4})& =(\color{red}{q}+\color{orange}{\frac{13}{11}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{13}{11})} . \color{green}{(x)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qx+2q+\frac{13}{11}x+\frac{13}{11}.2& \text{Uitwerken } \\ & =qx+2q+\frac{13}{11}x+\frac{26}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-12}{4}-x)(a-\frac{-3}{19})& =(\color{red}{-x}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{19}x-3a-3.\frac{3}{19}& \text{Uitwerken } \\ & =-ax-\frac{3}{19}x-3a-\frac{9}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{5}{10})(q-\frac{19}{17})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{17}p+\frac{1}{2}q-\frac{1}{2}.\frac{19}{17}& \text{Uitwerken } \\ & =pq-\frac{19}{17}p+\frac{1}{2}q-\frac{19}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{17}{10})(\frac{8}{4}+x)& =(\color{red}{p}+\color{orange}{\frac{-17}{10}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-17}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = px+2p-\frac{17}{10}x-\frac{17}{10}.2& \text{Uitwerken } \\ & =px+2p-\frac{17}{10}x-\frac{34}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+2p-\frac{17}{10}x-\frac{17}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{1}{10}-x)(b-\frac{2}{10})& =(\color{red}{-x}+\color{orange}{\frac{1}{10}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{1}{10})} . \color{green}{(b)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{5}x+\frac{1}{10}b-\frac{1}{10}.\frac{1}{5}& \text{Uitwerken } \\ & =-bx+\frac{1}{5}x+\frac{1}{10}b-\frac{1}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-09 18:22:12
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