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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{2}{18})(\frac{-14}{6}-b)& =(\color{red}{q}+\color{orange}{\frac{1}{9}}).(\color{green}{-b}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{1}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{3}q-\frac{1}{9}b-\frac{1}{9}.\frac{7}{3}& \text{Uitwerken } \\ & =-bq-\frac{7}{3}q-\frac{1}{9}b-\frac{7}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-14}{11})(x+\frac{3}{7})& =(\color{red}{a}+\color{orange}{\frac{14}{11}}).(\color{green}{x}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{14}{11})} . \color{green}{(x)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{7}a+\frac{14}{11}x+\frac{14}{11}.\frac{3}{7}& \text{Uitwerken } \\ & =ax+\frac{3}{7}a+\frac{14}{11}x+\frac{42}{77} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{7}a+\frac{14}{11}x+\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+\frac{10}{8})(p+\frac{7}{18})& =(\color{red}{b}+\color{orange}{\frac{5}{4}}).(\color{green}{p}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{18}b+\frac{5}{4}p+\frac{5}{4}.\frac{7}{18}& \text{Uitwerken } \\ & =bp+\frac{7}{18}b+\frac{5}{4}p+\frac{35}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{10}{15}-b)(\frac{3}{17}+b)& =(\color{red}{-b}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{3}{17}b+\frac{2}{3}b+\frac{2}{3}.\frac{3}{17}& \text{Uitwerken } \\ & =-b^2+((\frac{-3}{17})+\frac{2}{3})b+(\frac{-6}{51}) & \text{Neem samen} \\ &=-b^2+\frac{25}{51}b+(\frac{-6}{51}) & \text{Maak de som} \\ &=-b^2+\frac{25}{51}b+(\frac{-2}{17}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-3}{19}-p)(p+\frac{17}{10})& =(\color{red}{-p}+\color{orange}{\frac{-3}{19}}).(\color{green}{p}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{-3}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{17}{10}p-\frac{3}{19}p-\frac{3}{19}.\frac{17}{10}& \text{Uitwerken } \\ & =-p^2+((\frac{-17}{10})+(\frac{-3}{19}))p-\frac{51}{190} & \text{Neem samen} \\ &=-p^2-\frac{353}{190}p-\frac{51}{190} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(a-\frac{19}{12})(\frac{10}{8}-p)& =(\color{red}{a}+\color{orange}{\frac{-19}{12}}).(\color{green}{-p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{4}a+\frac{19}{12}p-\frac{19}{12}.\frac{5}{4}& \text{Uitwerken } \\ & =-ap+\frac{5}{4}a+\frac{19}{12}p-\frac{95}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{5}{2})(x-\frac{-6}{15})& =(\color{red}{a}+\color{orange}{\frac{5}{2}}).(\color{green}{x}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{5}a+\frac{5}{2}x+\frac{5}{2}.\frac{2}{5}& \text{Uitwerken } \\ & =ax+\frac{2}{5}a+\frac{5}{2}x+\frac{10}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{5}a+\frac{5}{2}x+1 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-8}{15}-x)(\frac{-16}{3}+a)& =(\color{red}{-x}+\color{orange}{\frac{-8}{15}}).(\color{green}{a}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{16}{3}x-\frac{8}{15}a+\frac{8}{15}.\frac{16}{3}& \text{Uitwerken } \\ & =-ax+\frac{16}{3}x-\frac{8}{15}a+\frac{128}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-18}{8})(a-\frac{2}{18})& =(\color{red}{a}+\color{orange}{\frac{9}{4}}).(\color{green}{a}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{9}a+\frac{9}{4}a-\frac{9}{4}.\frac{1}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{9})+\frac{9}{4})a-(\frac{-9}{36}) & \text{Neem samen} \\ &=a^2+\frac{77}{36}a-(\frac{-9}{36}) & \text{Maak de som} \\ &=a^2+\frac{77}{36}a+\frac{1}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(\frac{-8}{15}+x)(\frac{11}{10}-x)& =(\color{red}{x}+\color{orange}{\frac{-8}{15}}).(\color{green}{-x}+\color{blue}{\frac{11}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{10})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{11}{10})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{11}{10}x+\frac{8}{15}x-\frac{8}{15}.\frac{11}{10}& \text{Uitwerken } \\ & =-x^2+(\frac{11}{10}+\frac{8}{15})x-\frac{88}{150} & \text{Neem samen} \\ &=-x^2+\frac{49}{30}x-\frac{88}{150} & \text{Maak de som} \\ &=-x^2+\frac{49}{30}x-\frac{44}{75} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{12}-a)(p-\frac{-18}{20})& =(\color{red}{-a}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{10}a+\frac{1}{3}p+\frac{1}{3}.\frac{9}{10}& \text{Uitwerken } \\ & =-ap-\frac{9}{10}a+\frac{1}{3}p+\frac{9}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{9}{10}a+\frac{1}{3}p+\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-9}{11}-a)(a+\frac{-11}{14})& =(\color{red}{-a}+\color{orange}{\frac{-9}{11}}).(\color{green}{a}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{11}{14}a-\frac{9}{11}a+\frac{9}{11}.\frac{11}{14}& \text{Uitwerken } \\ & =-a^2+(\frac{11}{14}+(\frac{-9}{11}))a+(\frac{-99}{154}) & \text{Neem samen} \\ &=-a^2-\frac{5}{154}a+(\frac{-99}{154}) & \text{Maak de som} \\ &=-a^2-\frac{5}{154}a+(\frac{-9}{14}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-17 16:23:30
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