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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{18}{6})(\frac{-11}{20}+x)& =(\color{red}{q}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{20}q+3x-3.\frac{11}{20}& \text{Uitwerken } \\ & =qx-\frac{11}{20}q+3x-\frac{33}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+9)(x-\frac{-4}{2})& =(\color{red}{a}+\color{orange}{9}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(9)} . \color{green}{(x)} + \color{orange}{(9)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2a+9x+9.2& \text{Uitwerken } \\ & =ax+2a+9x+18 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-3}{20})(p+\frac{1}{12})& =(\color{red}{x}+\color{orange}{\frac{3}{20}}).(\color{green}{p}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{3}{20})} . \color{green}{(p)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{12}x+\frac{3}{20}p+\frac{3}{20}.\frac{1}{12}& \text{Uitwerken } \\ & =px+\frac{1}{12}x+\frac{3}{20}p+\frac{3}{240} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{12}x+\frac{3}{20}p+\frac{1}{80} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{3}-x)(\frac{8}{12}+x)& =(\color{red}{-x}+\color{orange}{\frac{11}{3}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{11}{3})} . \color{green}{(x)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{2}{3}x+\frac{11}{3}x+\frac{11}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-x^2+((\frac{-2}{3})+\frac{11}{3})x+(\frac{-22}{9}) & \text{Neem samen} \\ &=-x^2+\frac{9}{3}x+(\frac{-22}{9}) & \text{Maak de som} \\ &=-x^2+3x+(\frac{-22}{9}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{20}+a)(\frac{-12}{5}+x)& =(\color{red}{a}+\color{orange}{\frac{-3}{10}}).(\color{green}{x}+\color{blue}{\frac{-12}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{5})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{-12}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{12}{5}a-\frac{3}{10}x+\frac{3}{10}.\frac{12}{5}& \text{Uitwerken } \\ & =ax-\frac{12}{5}a-\frac{3}{10}x+\frac{36}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{12}{5}a-\frac{3}{10}x+\frac{18}{25} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-5}{7}-x)(b-\frac{4}{7})& =(\color{red}{-x}+\color{orange}{\frac{-5}{7}}).(\color{green}{b}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{4}{7}x-\frac{5}{7}b+\frac{5}{7}.\frac{4}{7}& \text{Uitwerken } \\ & =-bx+\frac{4}{7}x-\frac{5}{7}b+\frac{20}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{2}+x)(x+\frac{-9}{10})& =(\color{red}{x}+\color{orange}{\frac{13}{2}}).(\color{green}{x}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{13}{2})} . \color{green}{(x)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{9}{10}x+\frac{13}{2}x-\frac{13}{2}.\frac{9}{10}& \text{Uitwerken } \\ & =x^2+((\frac{-9}{10})+\frac{13}{2})x-(\frac{-117}{20}) & \text{Neem samen} \\ &=x^2+\frac{56}{10}x-(\frac{-117}{20}) & \text{Maak de som} \\ &=x^2+\frac{28}{5}x+\frac{117}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(\frac{11}{5}-p)(x+\frac{8}{19})& =(\color{red}{-p}+\color{orange}{\frac{11}{5}}).(\color{green}{x}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{11}{5})} . \color{green}{(x)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{8}{19}p+\frac{11}{5}x+\frac{11}{5}.\frac{8}{19}& \text{Uitwerken } \\ & =-px-\frac{8}{19}p+\frac{11}{5}x+\frac{88}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-17}{3})(\frac{5}{5}+b)& =(\color{red}{b}+\color{orange}{\frac{-17}{3}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-17}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bb+1b-\frac{17}{3}b-\frac{17}{3}.1& \text{Uitwerken } \\ & =b^2+(1+(\frac{-17}{3}))b-(\frac{-17}{3}) & \text{Neem samen} \\ &=b^2-\frac{14}{3}b-(\frac{-17}{3}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(x+\frac{19}{20})(a+\frac{-2}{8})& =(\color{red}{x}+\color{orange}{\frac{19}{20}}).(\color{green}{a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{19}{20})} . \color{green}{(a)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{4}x+\frac{19}{20}a-\frac{19}{20}.\frac{1}{4}& \text{Uitwerken } \\ & =ax-\frac{1}{4}x+\frac{19}{20}a-\frac{19}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{2}+a)(q-\frac{-14}{12})& =(\color{red}{a}+\color{orange}{(-7)}).(\color{green}{q}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(-7)} . \color{green}{(q)} + \color{orange}{(-7)} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{6}a-7q-7.\frac{7}{6}& \text{Uitwerken } \\ & =aq+\frac{7}{6}a-7q-\frac{49}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-3}{4}-a)(a-\frac{7}{3})& =(\color{red}{-a}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{7}{3}a-\frac{3}{4}a+\frac{3}{4}.\frac{7}{3}& \text{Uitwerken } \\ & =-a^2+(\frac{7}{3}+(\frac{-3}{4}))a+(\frac{-21}{12}) & \text{Neem samen} \\ &=-a^2+\frac{19}{12}a+(\frac{-21}{12}) & \text{Maak de som} \\ &=-a^2+\frac{19}{12}a+(\frac{-7}{4}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-28 20:44:34
Een site van Busleyden Atheneum Mechelen