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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{18}{6})(\frac{1}{6}-x)& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{-x}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(-3)} . \color{green}{(-x)} + \color{orange}{(-3)} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{6}x+3x-3.\frac{1}{6}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{6}+3)x-\frac{3}{6} & \text{Neem samen} \\ &=-x^2+\frac{19}{6}x-\frac{3}{6} & \text{Maak de som} \\ &=-x^2+\frac{19}{6}x-\frac{1}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{11}{9}+q)(\frac{-7}{11}-p)& =(\color{red}{q}+\color{orange}{\frac{11}{9}}).(\color{green}{-p}+\color{blue}{\frac{-7}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{11})} + \color{orange}{(\frac{11}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-7}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{7}{11}q-\frac{11}{9}p-\frac{11}{9}.\frac{7}{11}& \text{Uitwerken } \\ & =-pq-\frac{7}{11}q-\frac{11}{9}p-\frac{77}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{7}{11}q-\frac{11}{9}p-\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-13}{9})(b+\frac{19}{10})& =(\color{red}{b}+\color{orange}{\frac{13}{9}}).(\color{green}{b}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{13}{9})} . \color{green}{(b)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{19}{10}b+\frac{13}{9}b+\frac{13}{9}.\frac{19}{10}& \text{Uitwerken } \\ & =b^2+(\frac{19}{10}+\frac{13}{9})b+\frac{247}{90} & \text{Neem samen} \\ &=b^2+\frac{301}{90}b+\frac{247}{90} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-14}{19}-q)(q-\frac{10}{19})& =(\color{red}{-q}+\color{orange}{\frac{-14}{19}}).(\color{green}{q}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{10}{19}q-\frac{14}{19}q+\frac{14}{19}.\frac{10}{19}& \text{Uitwerken } \\ & =-q^2+(\frac{10}{19}+(\frac{-14}{19}))q+(\frac{-140}{361}) & \text{Neem samen} \\ &=-q^2-\frac{4}{19}q+(\frac{-140}{361}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-9}{15})(\frac{1}{6}-x)& =(\color{red}{x}+\color{orange}{\frac{-3}{5}}).(\color{green}{-x}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{6}x+\frac{3}{5}x-\frac{3}{5}.\frac{1}{6}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{6}+\frac{3}{5})x-\frac{3}{30} & \text{Neem samen} \\ &=-x^2+\frac{23}{30}x-\frac{3}{30} & \text{Maak de som} \\ &=-x^2+\frac{23}{30}x-\frac{1}{10} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{3}{18}+q)(b+\frac{-6}{18})& =(\color{red}{q}+\color{orange}{\frac{1}{6}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{3}q+\frac{1}{6}b-\frac{1}{6}.\frac{1}{3}& \text{Uitwerken } \\ & =bq-\frac{1}{3}q+\frac{1}{6}b-\frac{1}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{17}{20})(\frac{-7}{8}+a)& =(\color{red}{x}+\color{orange}{\frac{17}{20}}).(\color{green}{a}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{17}{20})} . \color{green}{(a)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{8}x+\frac{17}{20}a-\frac{17}{20}.\frac{7}{8}& \text{Uitwerken } \\ & =ax-\frac{7}{8}x+\frac{17}{20}a-\frac{119}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{14}{17})(\frac{6}{14}-q)& =(\color{red}{q}+\color{orange}{\frac{14}{17}}).(\color{green}{-q}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{14}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{3}{7}q-\frac{14}{17}q+\frac{14}{17}.\frac{3}{7}& \text{Uitwerken } \\ & =-q^2+(\frac{3}{7}+(\frac{-14}{17}))q+(\frac{-42}{119}) & \text{Neem samen} \\ &=-q^2-\frac{47}{119}q+(\frac{-42}{119}) & \text{Maak de som} \\ &=-q^2-\frac{47}{119}q+(\frac{-6}{17}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(a-\frac{8}{17})(\frac{5}{13}+x)& =(\color{red}{a}+\color{orange}{\frac{-8}{17}}).(\color{green}{x}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{13}a-\frac{8}{17}x-\frac{8}{17}.\frac{5}{13}& \text{Uitwerken } \\ & =ax+\frac{5}{13}a-\frac{8}{17}x-\frac{40}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{9}{14})(q-\frac{-7}{18})& =(\color{red}{p}+\color{orange}{\frac{9}{14}}).(\color{green}{q}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{9}{14})} . \color{green}{(q)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{18}p+\frac{9}{14}q+\frac{9}{14}.\frac{7}{18}& \text{Uitwerken } \\ & =pq+\frac{7}{18}p+\frac{9}{14}q+\frac{63}{252} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{7}{18}p+\frac{9}{14}q+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-6}{2})(x+\frac{-17}{2})& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{x}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(-3)} . \color{green}{(x)} + \color{orange}{(-3)} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{17}{2}x-3x+3.\frac{17}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-17}{2})+(-3))x+\frac{51}{2} & \text{Neem samen} \\ &=x^2-\frac{23}{2}x+\frac{51}{2} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(p+\frac{20}{5})(q+\frac{20}{12})& =(\color{red}{p}+\color{orange}{4}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{3}p+4q+4.\frac{5}{3}& \text{Uitwerken } \\ & =pq+\frac{5}{3}p+4q+\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-20 00:57:19
Een site van Busleyden Atheneum Mechelen