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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{7}{4})(\frac{-8}{18}+x)& =(\color{red}{b}+\color{orange}{\frac{-7}{4}}).(\color{green}{x}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{4}{9}b-\frac{7}{4}x+\frac{7}{4}.\frac{4}{9}& \text{Uitwerken } \\ & =bx-\frac{4}{9}b-\frac{7}{4}x+\frac{28}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{4}{9}b-\frac{7}{4}x+\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p+18)(\frac{-1}{17}-b)& =(\color{red}{p}+\color{orange}{18}).(\color{green}{-b}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(18)} . \color{green}{(-b)} + \color{orange}{(18)} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{17}p-18b-18.\frac{1}{17}& \text{Uitwerken } \\ & =-bp-\frac{1}{17}p-18b-\frac{18}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{5}{6}-q)(\frac{12}{6}-a)& =(\color{red}{-q}+\color{orange}{\frac{5}{6}}).(\color{green}{-a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{5}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq-2q-\frac{5}{6}a+\frac{5}{6}.2& \text{Uitwerken } \\ & =aq-2q-\frac{5}{6}a+\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-2q-\frac{5}{6}a+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-7}{5}-a)(x-\frac{17}{3})& =(\color{red}{-a}+\color{orange}{\frac{-7}{5}}).(\color{green}{x}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{17}{3}a-\frac{7}{5}x+\frac{7}{5}.\frac{17}{3}& \text{Uitwerken } \\ & =-ax+\frac{17}{3}a-\frac{7}{5}x+\frac{119}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{12}{18}+p)(q-\frac{-14}{17})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{14}{17}p+\frac{2}{3}q+\frac{2}{3}.\frac{14}{17}& \text{Uitwerken } \\ & =pq+\frac{14}{17}p+\frac{2}{3}q+\frac{28}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{16}{15})(x-\frac{16}{4})& =(\color{red}{a}+\color{orange}{\frac{-16}{15}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-16}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ax-4a-\frac{16}{15}x+\frac{16}{15}.4& \text{Uitwerken } \\ & =ax-4a-\frac{16}{15}x+\frac{64}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}((-1)-q)(b-\frac{-8}{9})& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{8}{9}q-1b-1.\frac{8}{9}& \text{Uitwerken } \\ & =-bq-\frac{8}{9}q-1b-\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-20}{4})(\frac{-17}{12}+a)& =(\color{red}{q}+\color{orange}{5}).(\color{green}{a}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(5)} . \color{green}{(a)} + \color{orange}{(5)} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{12}q+5a-5.\frac{17}{12}& \text{Uitwerken } \\ & =aq-\frac{17}{12}q+5a-\frac{85}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-12}{20})(\frac{9}{8}-x)& =(\color{red}{a}+\color{orange}{\frac{-3}{5}}).(\color{green}{-x}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{8}a+\frac{3}{5}x-\frac{3}{5}.\frac{9}{8}& \text{Uitwerken } \\ & =-ax+\frac{9}{8}a+\frac{3}{5}x-\frac{27}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(14-a)(a+\frac{-16}{3})& =(\color{red}{-a}+\color{orange}{14}).(\color{green}{a}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(14)} . \color{green}{(a)} + \color{orange}{(14)} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{16}{3}a+14a-14.\frac{16}{3}& \text{Uitwerken } \\ & =-a^2+(\frac{16}{3}+14)a-\frac{224}{3} & \text{Neem samen} \\ &=-a^2+\frac{58}{3}a-\frac{224}{3} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(x-\frac{20}{12})(\frac{-1}{10}+x)& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{10}x-\frac{5}{3}x+\frac{5}{3}.\frac{1}{10}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{10})+(\frac{-5}{3}))x+\frac{5}{30} & \text{Neem samen} \\ &=x^2-\frac{53}{30}x+\frac{5}{30} & \text{Maak de som} \\ &=x^2-\frac{53}{30}x+\frac{1}{6} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{5}{8}-p)(x+\frac{-11}{16})& =(\color{red}{-p}+\color{orange}{\frac{5}{8}}).(\color{green}{x}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(\frac{5}{8})} . \color{green}{(x)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{11}{16}p+\frac{5}{8}x-\frac{5}{8}.\frac{11}{16}& \text{Uitwerken } \\ & =-px+\frac{11}{16}p+\frac{5}{8}x-\frac{55}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-18 07:22:37
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