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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{2}{10}+p)(b-\frac{-16}{15})& =(\color{red}{p}+\color{orange}{\frac{1}{5}}).(\color{green}{b}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{16}{15}p+\frac{1}{5}b+\frac{1}{5}.\frac{16}{15}& \text{Uitwerken } \\ & =bp+\frac{16}{15}p+\frac{1}{5}b+\frac{16}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-13}{14})(a+\frac{2}{9})& =(\color{red}{q}+\color{orange}{\frac{13}{14}}).(\color{green}{a}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{13}{14})} . \color{green}{(a)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{9}q+\frac{13}{14}a+\frac{13}{14}.\frac{2}{9}& \text{Uitwerken } \\ & =aq+\frac{2}{9}q+\frac{13}{14}a+\frac{26}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{2}{9}q+\frac{13}{14}a+\frac{13}{63} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-5}{10}-p)(\frac{-6}{8}+p)& =(\color{red}{-p}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{3}{4}p-\frac{1}{2}p+\frac{1}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{3}{4}+(\frac{-1}{2}))p+(\frac{-3}{8}) & \text{Neem samen} \\ &=-p^2+\frac{1}{4}p+(\frac{-3}{8}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-12}{13})(\frac{10}{2}-a)& =(\color{red}{x}+\color{orange}{\frac{12}{13}}).(\color{green}{-a}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(5)} + \color{orange}{(\frac{12}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{12}{13})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -ax+5x-\frac{12}{13}a+\frac{12}{13}.5& \text{Uitwerken } \\ & =-ax+5x-\frac{12}{13}a+\frac{60}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-8}{2}+q)(\frac{-2}{12}-b)& =(\color{red}{q}+\color{orange}{(-4)}).(\color{green}{-b}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(-4)} . \color{green}{(-b)} + \color{orange}{(-4)} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{6}q+4b+4.\frac{1}{6}& \text{Uitwerken } \\ & =-bq-\frac{1}{6}q+4b+\frac{4}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{6}q+4b+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{5}+q)(b-\frac{-13}{9})& =(\color{red}{q}+\color{orange}{\frac{-7}{5}}).(\color{green}{b}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{9}q-\frac{7}{5}b-\frac{7}{5}.\frac{13}{9}& \text{Uitwerken } \\ & =bq+\frac{13}{9}q-\frac{7}{5}b-\frac{91}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{8}{3})(q-5)& =(\color{red}{x}+\color{orange}{\frac{8}{3}}).(\color{green}{q}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-5)} + \color{orange}{(\frac{8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = qx-5x+\frac{8}{3}q-\frac{8}{3}.5& \text{Uitwerken } \\ & =qx-5x+\frac{8}{3}q-\frac{40}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{13}{12})(\frac{-1}{13}+a)& =(\color{red}{a}+\color{orange}{\frac{-13}{12}}).(\color{green}{a}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{13}a-\frac{13}{12}a+\frac{13}{12}.\frac{1}{13}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{13})+(\frac{-13}{12}))a+\frac{13}{156} & \text{Neem samen} \\ &=a^2-\frac{181}{156}a+\frac{13}{156} & \text{Maak de som} \\ &=a^2-\frac{181}{156}a+\frac{1}{12} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-2}{5})(q+\frac{-17}{6})& =(\color{red}{a}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{6}a-\frac{2}{5}q+\frac{2}{5}.\frac{17}{6}& \text{Uitwerken } \\ & =aq-\frac{17}{6}a-\frac{2}{5}q+\frac{34}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{17}{6}a-\frac{2}{5}q+\frac{17}{15} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x+\frac{1}{9})(\frac{-3}{15}+q)& =(\color{red}{x}+\color{orange}{\frac{1}{9}}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{1}{9})} . \color{green}{(q)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{5}x+\frac{1}{9}q-\frac{1}{9}.\frac{1}{5}& \text{Uitwerken } \\ & =qx-\frac{1}{5}x+\frac{1}{9}q-\frac{1}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-9}{7}-a)(a+\frac{-15}{9})& =(\color{red}{-a}+\color{orange}{\frac{-9}{7}}).(\color{green}{a}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{5}{3}a-\frac{9}{7}a+\frac{9}{7}.\frac{5}{3}& \text{Uitwerken } \\ & =-a^2+(\frac{5}{3}+(\frac{-9}{7}))a+(\frac{-45}{21}) & \text{Neem samen} \\ &=-a^2+\frac{8}{21}a+(\frac{-45}{21}) & \text{Maak de som} \\ &=-a^2+\frac{8}{21}a+(\frac{-15}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{3}+x)(\frac{3}{19}+a)& =(\color{red}{x}+\color{orange}{\frac{-10}{3}}).(\color{green}{a}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{19}x-\frac{10}{3}a-\frac{10}{3}.\frac{3}{19}& \text{Uitwerken } \\ & =ax+\frac{3}{19}x-\frac{10}{3}a-\frac{30}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{19}x-\frac{10}{3}a-\frac{10}{19} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-22 16:28:52
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