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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{19}+x)(\frac{-15}{3}+b)& =(\color{red}{x}+\color{orange}{\frac{-13}{19}}).(\color{green}{b}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-5)} + \color{orange}{(\frac{-13}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = bx-5x-\frac{13}{19}b+\frac{13}{19}.5& \text{Uitwerken } \\ & =bx-5x-\frac{13}{19}b+\frac{65}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{6}{7})(\frac{-16}{19}-q)& =(\color{red}{b}+\color{orange}{\frac{6}{7}}).(\color{green}{-q}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{6}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{16}{19}b-\frac{6}{7}q-\frac{6}{7}.\frac{16}{19}& \text{Uitwerken } \\ & =-bq-\frac{16}{19}b-\frac{6}{7}q-\frac{96}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{13}{11}-a)(\frac{11}{20}+a)& =(\color{red}{-a}+\color{orange}{\frac{13}{11}}).(\color{green}{a}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{13}{11})} . \color{green}{(a)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{11}{20}a+\frac{13}{11}a+\frac{13}{11}.\frac{11}{20}& \text{Uitwerken } \\ & =-a^2+((\frac{-11}{20})+\frac{13}{11})a+(\frac{-143}{220}) & \text{Neem samen} \\ &=-a^2+\frac{139}{220}a+(\frac{-143}{220}) & \text{Maak de som} \\ &=-a^2+\frac{139}{220}a+(\frac{-13}{20}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{-6}{19}-b)(b+\frac{-9}{14})& =(\color{red}{-b}+\color{orange}{\frac{-6}{19}}).(\color{green}{b}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-6}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{19})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{9}{14}b-\frac{6}{19}b+\frac{6}{19}.\frac{9}{14}& \text{Uitwerken } \\ & =-b^2+(\frac{9}{14}+(\frac{-6}{19}))b+(\frac{-54}{266}) & \text{Neem samen} \\ &=-b^2+\frac{87}{266}b+(\frac{-54}{266}) & \text{Maak de som} \\ &=-b^2+\frac{87}{266}b+(\frac{-27}{133}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{8}{4}-b)(p-\frac{-13}{5})& =(\color{red}{-b}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{13}{5}b+2p+2.\frac{13}{5}& \text{Uitwerken } \\ & =-bp-\frac{13}{5}b+2p+\frac{26}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{17}{15})(\frac{3}{2}-q)& =(\color{red}{b}+\color{orange}{\frac{17}{15}}).(\color{green}{-q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{17}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{2}b-\frac{17}{15}q+\frac{17}{15}.\frac{3}{2}& \text{Uitwerken } \\ & =-bq+\frac{3}{2}b-\frac{17}{15}q+\frac{51}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{3}{2}b-\frac{17}{15}q+\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{19}{9}+p)(\frac{-10}{5}-p)& =(\color{red}{p}+\color{orange}{\frac{19}{9}}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{19}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -pp-2p-\frac{19}{9}p-\frac{19}{9}.2& \text{Uitwerken } \\ & =-p^2+((-2)+(\frac{-19}{9}))p-\frac{38}{9} & \text{Neem samen} \\ &=-p^2-\frac{37}{9}p-\frac{38}{9} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-3}{12})(\frac{-12}{10}+b)& =(\color{red}{x}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{6}{5}x-\frac{1}{4}b+\frac{1}{4}.\frac{6}{5}& \text{Uitwerken } \\ & =bx-\frac{6}{5}x-\frac{1}{4}b+\frac{6}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{6}{5}x-\frac{1}{4}b+\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{14}{2})(\frac{10}{12}-q)& =(\color{red}{x}+\color{orange}{(-7)}).(\color{green}{-q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(-7)} . \color{green}{(-q)} + \color{orange}{(-7)} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{6}x+7q-7.\frac{5}{6}& \text{Uitwerken } \\ & =-qx+\frac{5}{6}x+7q-\frac{35}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{12}{6}+p)(b+\frac{-6}{12})& =(\color{red}{p}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{2}p+2b-2.\frac{1}{2}& \text{Uitwerken } \\ & =bp-\frac{1}{2}p+2b-\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{1}{2}p+2b-1 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-20}{9})(x-\frac{-14}{9})& =(\color{red}{x}+\color{orange}{\frac{20}{9}}).(\color{green}{x}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{20}{9})} . \color{green}{(x)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{14}{9}x+\frac{20}{9}x+\frac{20}{9}.\frac{14}{9}& \text{Uitwerken } \\ & =x^2+(\frac{14}{9}+\frac{20}{9})x+\frac{280}{81} & \text{Neem samen} \\ &=x^2+\frac{34}{9}x+\frac{280}{81} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(x+\frac{14}{13})(b+\frac{14}{16})& =(\color{red}{x}+\color{orange}{\frac{14}{13}}).(\color{green}{b}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{14}{13})} . \color{green}{(b)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{8}x+\frac{14}{13}b+\frac{14}{13}.\frac{7}{8}& \text{Uitwerken } \\ & =bx+\frac{7}{8}x+\frac{14}{13}b+\frac{98}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{7}{8}x+\frac{14}{13}b+\frac{49}{52} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-03 11:32:46
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