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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{4}{2})(\frac{9}{13}+b)& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{13}a-2b-2.\frac{9}{13}& \text{Uitwerken } \\ & =ab+\frac{9}{13}a-2b-\frac{18}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{12}-x)(\frac{1}{9}-x)& =(\color{red}{-x}+\color{orange}{\frac{19}{12}}).(\color{green}{-x}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{19}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{9}x-\frac{19}{12}x+\frac{19}{12}.\frac{1}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{9})+(\frac{-19}{12}))x+\frac{19}{108} & \text{Neem samen} \\ &=x^2-\frac{61}{36}x+\frac{19}{108} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{19}{14}-x)(\frac{8}{5}-a)& =(\color{red}{-x}+\color{orange}{\frac{19}{14}}).(\color{green}{-a}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{19}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{8}{5}x-\frac{19}{14}a+\frac{19}{14}.\frac{8}{5}& \text{Uitwerken } \\ & =ax-\frac{8}{5}x-\frac{19}{14}a+\frac{152}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{8}{5}x-\frac{19}{14}a+\frac{76}{35} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{13}{19}-a)(\frac{2}{7}-a)& =(\color{red}{-a}+\color{orange}{\frac{13}{19}}).(\color{green}{-a}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{13}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{2}{7}a-\frac{13}{19}a+\frac{13}{19}.\frac{2}{7}& \text{Uitwerken } \\ & =a^2+((\frac{-2}{7})+(\frac{-13}{19}))a+\frac{26}{133} & \text{Neem samen} \\ &=a^2-\frac{129}{133}a+\frac{26}{133} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-20}{11}-a)(x+\frac{-13}{4})& =(\color{red}{-a}+\color{orange}{\frac{-20}{11}}).(\color{green}{x}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{4}a-\frac{20}{11}x+\frac{20}{11}.\frac{13}{4}& \text{Uitwerken } \\ & =-ax+\frac{13}{4}a-\frac{20}{11}x+\frac{260}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{13}{4}a-\frac{20}{11}x+\frac{65}{11} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-1}{2})(x-\frac{17}{11})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{11}p+\frac{1}{2}x-\frac{1}{2}.\frac{17}{11}& \text{Uitwerken } \\ & =px-\frac{17}{11}p+\frac{1}{2}x-\frac{17}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{20}{5})(\frac{12}{18}-p)& =(\color{red}{x}+\color{orange}{4}).(\color{green}{-p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(4)} . \color{green}{(-p)} + \color{orange}{(4)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{3}x-4p+4.\frac{2}{3}& \text{Uitwerken } \\ & =-px+\frac{2}{3}x-4p+\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-16}{13}+p)(x+16)& =(\color{red}{p}+\color{orange}{\frac{-16}{13}}).(\color{green}{x}+\color{blue}{16})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(16)} + \color{orange}{(\frac{-16}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = px+16p-\frac{16}{13}x-\frac{16}{13}.16& \text{Uitwerken } \\ & =px+16p-\frac{16}{13}x-\frac{256}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-18}{8})(a+\frac{-4}{14})& =(\color{red}{q}+\color{orange}{\frac{9}{4}}).(\color{green}{a}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{7}q+\frac{9}{4}a-\frac{9}{4}.\frac{2}{7}& \text{Uitwerken } \\ & =aq-\frac{2}{7}q+\frac{9}{4}a-\frac{18}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{2}{7}q+\frac{9}{4}a-\frac{9}{14} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{9}{14}-a)(\frac{20}{8}-x)& =(\color{red}{-a}+\color{orange}{\frac{9}{14}}).(\color{green}{-x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{9}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{2}a-\frac{9}{14}x+\frac{9}{14}.\frac{5}{2}& \text{Uitwerken } \\ & =ax-\frac{5}{2}a-\frac{9}{14}x+\frac{45}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-1}{6})(\frac{-17}{17}-p)& =(\color{red}{a}+\color{orange}{\frac{1}{6}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap-1a-\frac{1}{6}p-\frac{1}{6}.1& \text{Uitwerken } \\ & =-ap-1a-\frac{1}{6}p-\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{7}{11})(x-\frac{-15}{15})& =(\color{red}{q}+\color{orange}{\frac{7}{11}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{7}{11})} . \color{green}{(x)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx+1q+\frac{7}{11}x+\frac{7}{11}.1& \text{Uitwerken } \\ & =qx+1q+\frac{7}{11}x+\frac{7}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-14 13:39:53
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