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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{11}{8})(b+\frac{-13}{10})& =(\color{red}{b}+\color{orange}{\frac{-11}{8}}).(\color{green}{b}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{13}{10}b-\frac{11}{8}b+\frac{11}{8}.\frac{13}{10}& \text{Uitwerken } \\ & =b^2+((\frac{-13}{10})+(\frac{-11}{8}))b+\frac{143}{80} & \text{Neem samen} \\ &=b^2-\frac{107}{40}b+\frac{143}{80} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(x-\frac{5}{7})(x+\frac{-18}{19})& =(\color{red}{x}+\color{orange}{\frac{-5}{7}}).(\color{green}{x}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{18}{19}x-\frac{5}{7}x+\frac{5}{7}.\frac{18}{19}& \text{Uitwerken } \\ & =x^2+((\frac{-18}{19})+(\frac{-5}{7}))x+\frac{90}{133} & \text{Neem samen} \\ &=x^2-\frac{221}{133}x+\frac{90}{133} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(5+a)(b+\frac{-1}{12})& =(\color{red}{a}+\color{orange}{5}).(\color{green}{b}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(5)} . \color{green}{(b)} + \color{orange}{(5)} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{12}a+5b-5.\frac{1}{12}& \text{Uitwerken } \\ & =ab-\frac{1}{12}a+5b-\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{6}{18})(\frac{-2}{19}+a)& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{a}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{19}x-\frac{1}{3}a+\frac{1}{3}.\frac{2}{19}& \text{Uitwerken } \\ & =ax-\frac{2}{19}x-\frac{1}{3}a+\frac{2}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{9}{10})(\frac{6}{16}+b)& =(\color{red}{b}+\color{orange}{\frac{-9}{10}}).(\color{green}{b}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{8}b-\frac{9}{10}b-\frac{9}{10}.\frac{3}{8}& \text{Uitwerken } \\ & =b^2+(\frac{3}{8}+(\frac{-9}{10}))b-(\frac{-27}{80}) & \text{Neem samen} \\ &=b^2-\frac{21}{40}b-(\frac{-27}{80}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-15}{17})(\frac{-11}{5}-x)& =(\color{red}{x}+\color{orange}{\frac{-15}{17}}).(\color{green}{-x}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(\frac{-15}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{11}{5}x+\frac{15}{17}x+\frac{15}{17}.\frac{11}{5}& \text{Uitwerken } \\ & =-x^2+((\frac{-11}{5})+\frac{15}{17})x+(\frac{-165}{85}) & \text{Neem samen} \\ &=-x^2-\frac{112}{85}x+(\frac{-165}{85}) & \text{Maak de som} \\ &=-x^2-\frac{112}{85}x+(\frac{-33}{17}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(q-\frac{9}{9})(\frac{17}{6}-q)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{17}{6}q+1q-1.\frac{17}{6}& \text{Uitwerken } \\ & =-q^2+(\frac{17}{6}+1)q-\frac{17}{6} & \text{Neem samen} \\ &=-q^2+\frac{23}{6}q-\frac{17}{6} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{14}{14}+a)(\frac{-3}{19}-x)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{19}a-1x-1.\frac{3}{19}& \text{Uitwerken } \\ & =-ax-\frac{3}{19}a-1x-\frac{3}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-4}{16}-a)(\frac{-20}{12}-b)& =(\color{red}{-a}+\color{orange}{\frac{-1}{4}}).(\color{green}{-b}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{3}a+\frac{1}{4}b+\frac{1}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =ab+\frac{5}{3}a+\frac{1}{4}b+\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-11}{20})(q-\frac{-13}{15})& =(\color{red}{b}+\color{orange}{\frac{11}{20}}).(\color{green}{q}+\color{blue}{\frac{13}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{13}{15})} + \color{orange}{(\frac{11}{20})} . \color{green}{(q)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{13}{15})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{15}b+\frac{11}{20}q+\frac{11}{20}.\frac{13}{15}& \text{Uitwerken } \\ & =bq+\frac{13}{15}b+\frac{11}{20}q+\frac{143}{300} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-5}{6})(\frac{20}{4}+b)& =(\color{red}{b}+\color{orange}{\frac{-5}{6}}).(\color{green}{b}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(5)} + \color{orange}{(\frac{-5}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bb+5b-\frac{5}{6}b-\frac{5}{6}.5& \text{Uitwerken } \\ & =b^2+(5+(\frac{-5}{6}))b-(\frac{-25}{6}) & \text{Neem samen} \\ &=b^2+\frac{25}{6}b-(\frac{-25}{6}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-4}{5})(\frac{5}{11}-p)& =(\color{red}{q}+\color{orange}{\frac{-4}{5}}).(\color{green}{-p}+\color{blue}{\frac{5}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{11})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{5}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{11}q+\frac{4}{5}p-\frac{4}{5}.\frac{5}{11}& \text{Uitwerken } \\ & =-pq+\frac{5}{11}q+\frac{4}{5}p-\frac{20}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{5}{11}q+\frac{4}{5}p-\frac{4}{11} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-06 14:13:33
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