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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{12}{18}-q)(q-\frac{-19}{4})& =(\color{red}{-q}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{19}{4}q+\frac{2}{3}q+\frac{2}{3}.\frac{19}{4}& \text{Uitwerken } \\ & =-q^2+((\frac{-19}{4})+\frac{2}{3})q+(\frac{-38}{12}) & \text{Neem samen} \\ &=-q^2-\frac{49}{12}q+(\frac{-38}{12}) & \text{Maak de som} \\ &=-q^2-\frac{49}{12}q+(\frac{-19}{6}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{13}{12}-q)(\frac{-6}{11}+x)& =(\color{red}{-q}+\color{orange}{\frac{13}{12}}).(\color{green}{x}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{13}{12})} . \color{green}{(x)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{6}{11}q+\frac{13}{12}x-\frac{13}{12}.\frac{6}{11}& \text{Uitwerken } \\ & =-qx+\frac{6}{11}q+\frac{13}{12}x-\frac{78}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{6}{11}q+\frac{13}{12}x-\frac{13}{22} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{11}{6}-b)(q+\frac{-5}{14})& =(\color{red}{-b}+\color{orange}{\frac{11}{6}}).(\color{green}{q}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{11}{6})} . \color{green}{(q)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{14}b+\frac{11}{6}q-\frac{11}{6}.\frac{5}{14}& \text{Uitwerken } \\ & =-bq+\frac{5}{14}b+\frac{11}{6}q-\frac{55}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-15}{8}-x)(\frac{13}{11}-x)& =(\color{red}{-x}+\color{orange}{\frac{-15}{8}}).(\color{green}{-x}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{13}{11}x+\frac{15}{8}x-\frac{15}{8}.\frac{13}{11}& \text{Uitwerken } \\ & =x^2+((\frac{-13}{11})+\frac{15}{8})x-(\frac{-195}{88}) & \text{Neem samen} \\ &=x^2+\frac{61}{88}x-(\frac{-195}{88}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(x-\frac{5}{19})(\frac{-14}{20}-q)& =(\color{red}{x}+\color{orange}{\frac{-5}{19}}).(\color{green}{-q}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{7}{10}x+\frac{5}{19}q+\frac{5}{19}.\frac{7}{10}& \text{Uitwerken } \\ & =-qx-\frac{7}{10}x+\frac{5}{19}q+\frac{35}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{7}{10}x+\frac{5}{19}q+\frac{7}{38} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-12}{5})(\frac{8}{4}-x)& =(\color{red}{a}+\color{orange}{\frac{-12}{5}}).(\color{green}{-x}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-12}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-12}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ax+2a+\frac{12}{5}x-\frac{12}{5}.2& \text{Uitwerken } \\ & =-ax+2a+\frac{12}{5}x-\frac{24}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-20}{3})(\frac{1}{3}+x)& =(\color{red}{b}+\color{orange}{\frac{20}{3}}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{20}{3})} . \color{green}{(x)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{3}b+\frac{20}{3}x+\frac{20}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =bx+\frac{1}{3}b+\frac{20}{3}x+\frac{20}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{9}{10}-q)(a+\frac{-12}{10})& =(\color{red}{-q}+\color{orange}{\frac{9}{10}}).(\color{green}{a}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{9}{10})} . \color{green}{(a)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{6}{5}q+\frac{9}{10}a-\frac{9}{10}.\frac{6}{5}& \text{Uitwerken } \\ & =-aq+\frac{6}{5}q+\frac{9}{10}a-\frac{54}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{6}{5}q+\frac{9}{10}a-\frac{27}{25} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-15}{15})(x-\frac{9}{4})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{4}p+1x-1.\frac{9}{4}& \text{Uitwerken } \\ & =px-\frac{9}{4}p+1x-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-8}{5})(a+\frac{18}{17})& =(\color{red}{x}+\color{orange}{\frac{8}{5}}).(\color{green}{a}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{8}{5})} . \color{green}{(a)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{18}{17}x+\frac{8}{5}a+\frac{8}{5}.\frac{18}{17}& \text{Uitwerken } \\ & =ax+\frac{18}{17}x+\frac{8}{5}a+\frac{144}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{3}{13})(\frac{-14}{8}-q)& =(\color{red}{x}+\color{orange}{\frac{-3}{13}}).(\color{green}{-q}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{7}{4}x+\frac{3}{13}q+\frac{3}{13}.\frac{7}{4}& \text{Uitwerken } \\ & =-qx-\frac{7}{4}x+\frac{3}{13}q+\frac{21}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{19}{12}-q)(\frac{-14}{19}+q)& =(\color{red}{-q}+\color{orange}{\frac{19}{12}}).(\color{green}{q}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{19}{12})} . \color{green}{(q)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{14}{19}q+\frac{19}{12}q-\frac{19}{12}.\frac{14}{19}& \text{Uitwerken } \\ & =-q^2+(\frac{14}{19}+\frac{19}{12})q-\frac{266}{228} & \text{Neem samen} \\ &=-q^2+\frac{529}{228}q-\frac{266}{228} & \text{Maak de som} \\ &=-q^2+\frac{529}{228}q-\frac{7}{6} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-13 12:13:13
Een site van Busleyden Atheneum Mechelen