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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{6}{4})(a-\frac{-9}{8})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{9}{8}a+\frac{3}{2}a+\frac{3}{2}.\frac{9}{8}& \text{Uitwerken } \\ & =a^2+(\frac{9}{8}+\frac{3}{2})a+\frac{27}{16} & \text{Neem samen} \\ &=a^2+\frac{21}{8}a+\frac{27}{16} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{4}+p)(p-\frac{-3}{15})& =(\color{red}{p}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{5}p-3p-3.\frac{1}{5}& \text{Uitwerken } \\ & =p^2+(\frac{1}{5}+(-3))p-(\frac{-3}{5}) & \text{Neem samen} \\ &=p^2-\frac{14}{5}p-(\frac{-3}{5}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{7}{3}+q)(\frac{-1}{10}+b)& =(\color{red}{q}+\color{orange}{\frac{7}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{7}{3})} . \color{green}{(b)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{10}q+\frac{7}{3}b-\frac{7}{3}.\frac{1}{10}& \text{Uitwerken } \\ & =bq-\frac{1}{10}q+\frac{7}{3}b-\frac{7}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-3}{10}+x)(\frac{2}{20}+q)& =(\color{red}{x}+\color{orange}{\frac{-3}{10}}).(\color{green}{q}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{10}x-\frac{3}{10}q-\frac{3}{10}.\frac{1}{10}& \text{Uitwerken } \\ & =qx+\frac{1}{10}x-\frac{3}{10}q-\frac{3}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-8}{9}+p)(a-\frac{-8}{6})& =(\color{red}{p}+\color{orange}{\frac{-8}{9}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{3}p-\frac{8}{9}a-\frac{8}{9}.\frac{4}{3}& \text{Uitwerken } \\ & =ap+\frac{4}{3}p-\frac{8}{9}a-\frac{32}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-3}{19})(\frac{19}{7}+x)& =(\color{red}{p}+\color{orange}{\frac{3}{19}}).(\color{green}{x}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(\frac{3}{19})} . \color{green}{(x)} + \color{orange}{(\frac{3}{19})} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{19}{7}p+\frac{3}{19}x+\frac{3}{19}.\frac{19}{7}& \text{Uitwerken } \\ & =px+\frac{19}{7}p+\frac{3}{19}x+\frac{57}{133} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{19}{7}p+\frac{3}{19}x+\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-19}{11}+x)(\frac{-3}{11}-x)& =(\color{red}{x}+\color{orange}{\frac{-19}{11}}).(\color{green}{-x}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{3}{11}x+\frac{19}{11}x+\frac{19}{11}.\frac{3}{11}& \text{Uitwerken } \\ & =-x^2+((\frac{-3}{11})+\frac{19}{11})x+(\frac{-57}{121}) & \text{Neem samen} \\ &=-x^2+\frac{16}{11}x+(\frac{-57}{121}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-13}{10}+a)(\frac{-9}{6}-a)& =(\color{red}{a}+\color{orange}{\frac{-13}{10}}).(\color{green}{-a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{3}{2}a+\frac{13}{10}a+\frac{13}{10}.\frac{3}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-3}{2})+\frac{13}{10})a+(\frac{-39}{20}) & \text{Neem samen} \\ &=-a^2-\frac{2}{10}a+(\frac{-39}{20}) & \text{Maak de som} \\ &=-a^2-\frac{1}{5}a+(\frac{-39}{20}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(x-\frac{15}{4})(p-\frac{11}{13})& =(\color{red}{x}+\color{orange}{\frac{-15}{4}}).(\color{green}{p}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{13}x-\frac{15}{4}p+\frac{15}{4}.\frac{11}{13}& \text{Uitwerken } \\ & =px-\frac{11}{13}x-\frac{15}{4}p+\frac{165}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{5}{17}+q)(\frac{8}{15}+x)& =(\color{red}{q}+\color{orange}{\frac{5}{17}}).(\color{green}{x}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(\frac{5}{17})} . \color{green}{(x)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{8}{15}q+\frac{5}{17}x+\frac{5}{17}.\frac{8}{15}& \text{Uitwerken } \\ & =qx+\frac{8}{15}q+\frac{5}{17}x+\frac{40}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{8}{15}q+\frac{5}{17}x+\frac{8}{51} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{7}{2}+p)(x-\frac{13}{5})& =(\color{red}{p}+\color{orange}{\frac{7}{2}}).(\color{green}{x}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(\frac{7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{5}p+\frac{7}{2}x-\frac{7}{2}.\frac{13}{5}& \text{Uitwerken } \\ & =px-\frac{13}{5}p+\frac{7}{2}x-\frac{91}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{18}{19})(q+\frac{-11}{7})& =(\color{red}{a}+\color{orange}{\frac{-18}{19}}).(\color{green}{q}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{7}a-\frac{18}{19}q+\frac{18}{19}.\frac{11}{7}& \text{Uitwerken } \\ & =aq-\frac{11}{7}a-\frac{18}{19}q+\frac{198}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-21 19:53:18
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