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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-9}{16})(\frac{-7}{7}-x)& =(\color{red}{x}+\color{orange}{\frac{9}{16}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{9}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -xx-1x-\frac{9}{16}x-\frac{9}{16}.1& \text{Uitwerken } \\ & =-x^2+((-1)+(\frac{-9}{16}))x-\frac{9}{16} & \text{Neem samen} \\ &=-x^2-\frac{25}{16}x-\frac{9}{16} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-11}{17})(q+\frac{9}{20})& =(\color{red}{a}+\color{orange}{\frac{11}{17}}).(\color{green}{q}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{11}{17})} . \color{green}{(q)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{20}a+\frac{11}{17}q+\frac{11}{17}.\frac{9}{20}& \text{Uitwerken } \\ & =aq+\frac{9}{20}a+\frac{11}{17}q+\frac{99}{340} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{15}{20}+b)(b+\frac{-4}{8})& =(\color{red}{b}+\color{orange}{\frac{3}{4}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{2}b+\frac{3}{4}b-\frac{3}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{2})+\frac{3}{4})b-(\frac{-3}{8}) & \text{Neem samen} \\ &=b^2+\frac{1}{4}b-(\frac{-3}{8}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x-(-2))(b+\frac{13}{11})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{13}{11}x+2b+2.\frac{13}{11}& \text{Uitwerken } \\ & =bx+\frac{13}{11}x+2b+\frac{26}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{19}+q)(b-\frac{16}{15})& =(\color{red}{q}+\color{orange}{\frac{-10}{19}}).(\color{green}{b}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{16}{15}q-\frac{10}{19}b+\frac{10}{19}.\frac{16}{15}& \text{Uitwerken } \\ & =bq-\frac{16}{15}q-\frac{10}{19}b+\frac{160}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{16}{15}q-\frac{10}{19}b+\frac{32}{57} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{12}{20}+a)(x-\frac{-4}{6})& =(\color{red}{a}+\color{orange}{\frac{3}{5}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}a+\frac{3}{5}x+\frac{3}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}a+\frac{3}{5}x+\frac{6}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{3}a+\frac{3}{5}x+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-12}{16}-x)(\frac{10}{8}-a)& =(\color{red}{-x}+\color{orange}{\frac{-3}{4}}).(\color{green}{-a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{4}x+\frac{3}{4}a-\frac{3}{4}.\frac{5}{4}& \text{Uitwerken } \\ & =ax-\frac{5}{4}x+\frac{3}{4}a-\frac{15}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{7}{19})(\frac{14}{11}+b)& =(\color{red}{b}+\color{orange}{\frac{7}{19}}).(\color{green}{b}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{7}{19})} . \color{green}{(b)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{14}{11}b+\frac{7}{19}b+\frac{7}{19}.\frac{14}{11}& \text{Uitwerken } \\ & =b^2+(\frac{14}{11}+\frac{7}{19})b+\frac{98}{209} & \text{Neem samen} \\ &=b^2+\frac{343}{209}b+\frac{98}{209} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-18}{20}-a)(x+\frac{-14}{14})& =(\color{red}{-a}+\color{orange}{\frac{-9}{10}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-9}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ax+1a-\frac{9}{10}x+\frac{9}{10}.1& \text{Uitwerken } \\ & =-ax+1a-\frac{9}{10}x+\frac{9}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{13}{9})(\frac{9}{20}-p)& =(\color{red}{p}+\color{orange}{\frac{13}{9}}).(\color{green}{-p}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{13}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{9}{20}p-\frac{13}{9}p+\frac{13}{9}.\frac{9}{20}& \text{Uitwerken } \\ & =-p^2+(\frac{9}{20}+(\frac{-13}{9}))p+(\frac{-117}{180}) & \text{Neem samen} \\ &=-p^2-\frac{179}{180}p+(\frac{-117}{180}) & \text{Maak de som} \\ &=-p^2-\frac{179}{180}p+(\frac{-13}{20}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(q-\frac{18}{5})(\frac{-1}{8}+a)& =(\color{red}{q}+\color{orange}{\frac{-18}{5}}).(\color{green}{a}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{8}q-\frac{18}{5}a+\frac{18}{5}.\frac{1}{8}& \text{Uitwerken } \\ & =aq-\frac{1}{8}q-\frac{18}{5}a+\frac{18}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{8}q-\frac{18}{5}a+\frac{9}{20} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-17}{3}-a)(\frac{19}{18}+q)& =(\color{red}{-a}+\color{orange}{\frac{-17}{3}}).(\color{green}{q}+\color{blue}{\frac{19}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{18})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{19}{18})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{18}a-\frac{17}{3}q-\frac{17}{3}.\frac{19}{18}& \text{Uitwerken } \\ & =-aq-\frac{19}{18}a-\frac{17}{3}q-\frac{323}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-17 02:29:42
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