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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-11}{9}+a)(\frac{-8}{12}+x)& =(\color{red}{a}+\color{orange}{\frac{-11}{9}}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{3}a-\frac{11}{9}x+\frac{11}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =ax-\frac{2}{3}a-\frac{11}{9}x+\frac{22}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{18}{17})(\frac{-11}{19}-x)& =(\color{red}{x}+\color{orange}{\frac{-18}{17}}).(\color{green}{-x}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{11}{19}x+\frac{18}{17}x+\frac{18}{17}.\frac{11}{19}& \text{Uitwerken } \\ & =-x^2+((\frac{-11}{19})+\frac{18}{17})x+(\frac{-198}{323}) & \text{Neem samen} \\ &=-x^2+\frac{155}{323}x+(\frac{-198}{323}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(b-\frac{16}{4})(\frac{11}{15}+x)& =(\color{red}{b}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{15}b-4x-4.\frac{11}{15}& \text{Uitwerken } \\ & =bx+\frac{11}{15}b-4x-\frac{44}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{18}{9}+b)(a+\frac{-3}{19})& =(\color{red}{b}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{19}b+2a-2.\frac{3}{19}& \text{Uitwerken } \\ & =ab-\frac{3}{19}b+2a-\frac{6}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{18}+q)(\frac{-18}{4}-x)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{-x}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{9}{2}q-\frac{1}{2}x-\frac{1}{2}.\frac{9}{2}& \text{Uitwerken } \\ & =-qx-\frac{9}{2}q-\frac{1}{2}x-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{5}-a)(\frac{9}{20}-q)& =(\color{red}{-a}+\color{orange}{4}).(\color{green}{-q}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(4)} . \color{green}{(-q)} + \color{orange}{(4)} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{9}{20}a-4q+4.\frac{9}{20}& \text{Uitwerken } \\ & =aq-\frac{9}{20}a-4q+\frac{36}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{9}{20}a-4q+\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+\frac{-20}{16})(p+\frac{-16}{19})& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{p}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{16}{19}p-\frac{5}{4}p+\frac{5}{4}.\frac{16}{19}& \text{Uitwerken } \\ & =p^2+((\frac{-16}{19})+(\frac{-5}{4}))p+\frac{80}{76} & \text{Neem samen} \\ &=p^2-\frac{159}{76}p+\frac{80}{76} & \text{Maak de som} \\ &=p^2-\frac{159}{76}p+\frac{20}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(x-\frac{10}{6})(\frac{-1}{20}+x)& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{20}x-\frac{5}{3}x+\frac{5}{3}.\frac{1}{20}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{20})+(\frac{-5}{3}))x+\frac{5}{60} & \text{Neem samen} \\ &=x^2-\frac{103}{60}x+\frac{5}{60} & \text{Maak de som} \\ &=x^2-\frac{103}{60}x+\frac{1}{12} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-18}{7})(x-\frac{-19}{7})& =(\color{red}{q}+\color{orange}{\frac{18}{7}}).(\color{green}{x}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(\frac{18}{7})} . \color{green}{(x)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{7}q+\frac{18}{7}x+\frac{18}{7}.\frac{19}{7}& \text{Uitwerken } \\ & =qx+\frac{19}{7}q+\frac{18}{7}x+\frac{342}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{7}{12}-a)(\frac{10}{2}-b)& =(\color{red}{-a}+\color{orange}{\frac{7}{12}}).(\color{green}{-b}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(5)} + \color{orange}{(\frac{7}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = ab-5a-\frac{7}{12}b+\frac{7}{12}.5& \text{Uitwerken } \\ & =ab-5a-\frac{7}{12}b+\frac{35}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-11}{8}-a)(a+\frac{-8}{14})& =(\color{red}{-a}+\color{orange}{\frac{-11}{8}}).(\color{green}{a}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{4}{7}a-\frac{11}{8}a+\frac{11}{8}.\frac{4}{7}& \text{Uitwerken } \\ & =-a^2+(\frac{4}{7}+(\frac{-11}{8}))a+(\frac{-44}{56}) & \text{Neem samen} \\ &=-a^2-\frac{45}{56}a+(\frac{-44}{56}) & \text{Maak de som} \\ &=-a^2-\frac{45}{56}a+(\frac{-11}{14}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-11}{2})(\frac{-9}{7}-p)& =(\color{red}{a}+\color{orange}{\frac{-11}{2}}).(\color{green}{-p}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{-11}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{7}a+\frac{11}{2}p+\frac{11}{2}.\frac{9}{7}& \text{Uitwerken } \\ & =-ap-\frac{9}{7}a+\frac{11}{2}p+\frac{99}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-11 19:59:29
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