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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{17}{19})(\frac{-8}{5}-b)& =(\color{red}{x}+\color{orange}{\frac{17}{19}}).(\color{green}{-b}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{17}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{8}{5}x-\frac{17}{19}b-\frac{17}{19}.\frac{8}{5}& \text{Uitwerken } \\ & =-bx-\frac{8}{5}x-\frac{17}{19}b-\frac{136}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{12}-p)(\frac{-3}{14}+q)& =(\color{red}{-p}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{14}p+\frac{2}{3}q-\frac{2}{3}.\frac{3}{14}& \text{Uitwerken } \\ & =-pq+\frac{3}{14}p+\frac{2}{3}q-\frac{6}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{3}{14}p+\frac{2}{3}q-\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-6}{9}+p)(p+\frac{-18}{4})& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{9}{2}p-\frac{2}{3}p+\frac{2}{3}.\frac{9}{2}& \text{Uitwerken } \\ & =p^2+((\frac{-9}{2})+(\frac{-2}{3}))p+\frac{18}{6} & \text{Neem samen} \\ &=p^2-\frac{31}{6}p+\frac{18}{6} & \text{Maak de som} \\ &=p^2-\frac{31}{6}p+3 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{2}{12}+q)(\frac{-3}{9}+b)& =(\color{red}{q}+\color{orange}{\frac{1}{6}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{3}q+\frac{1}{6}b-\frac{1}{6}.\frac{1}{3}& \text{Uitwerken } \\ & =bq-\frac{1}{3}q+\frac{1}{6}b-\frac{1}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{14}{20}-b)(\frac{20}{7}-x)& =(\color{red}{-b}+\color{orange}{\frac{7}{10}}).(\color{green}{-x}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{7}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{20}{7}b-\frac{7}{10}x+\frac{7}{10}.\frac{20}{7}& \text{Uitwerken } \\ & =bx-\frac{20}{7}b-\frac{7}{10}x+\frac{140}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{20}{7}b-\frac{7}{10}x+2 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-15}{18}+x)(\frac{4}{15}-b)& =(\color{red}{x}+\color{orange}{\frac{-5}{6}}).(\color{green}{-b}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{4}{15}x+\frac{5}{6}b-\frac{5}{6}.\frac{4}{15}& \text{Uitwerken } \\ & =-bx+\frac{4}{15}x+\frac{5}{6}b-\frac{20}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{4}{15}x+\frac{5}{6}b-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{6}{15}-x)(p-\frac{7}{9})& =(\color{red}{-x}+\color{orange}{\frac{2}{5}}).(\color{green}{p}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{9}x+\frac{2}{5}p-\frac{2}{5}.\frac{7}{9}& \text{Uitwerken } \\ & =-px+\frac{7}{9}x+\frac{2}{5}p-\frac{14}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}((-4)-x)((-13)-q)& =(\color{red}{-x}+\color{orange}{(-4)}).(\color{green}{-q}+\color{blue}{(-13)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(-13)} + \color{orange}{(-4)} . \color{green}{(-q)} + \color{orange}{(-4)} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = qx+13x+4q+4.13& \text{Uitwerken } \\ & =qx+13x+4q+52 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-7}{10}-a)(\frac{-7}{19}+x)& =(\color{red}{-a}+\color{orange}{\frac{-7}{10}}).(\color{green}{x}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{19}a-\frac{7}{10}x+\frac{7}{10}.\frac{7}{19}& \text{Uitwerken } \\ & =-ax+\frac{7}{19}a-\frac{7}{10}x+\frac{49}{190} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-2}{11})(x-\frac{3}{2})& =(\color{red}{p}+\color{orange}{\frac{-2}{11}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{2}p-\frac{2}{11}x+\frac{2}{11}.\frac{3}{2}& \text{Uitwerken } \\ & =px-\frac{3}{2}p-\frac{2}{11}x+\frac{6}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{3}{2}p-\frac{2}{11}x+\frac{3}{11} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{14}{2})(b-\frac{7}{9})& =(\color{red}{x}+\color{orange}{7}).(\color{green}{b}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(7)} . \color{green}{(b)} + \color{orange}{(7)} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{9}x+7b-7.\frac{7}{9}& \text{Uitwerken } \\ & =bx-\frac{7}{9}x+7b-\frac{49}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p+\frac{10}{6})(\frac{-6}{20}+q)& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{q}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{10}p+\frac{5}{3}q-\frac{5}{3}.\frac{3}{10}& \text{Uitwerken } \\ & =pq-\frac{3}{10}p+\frac{5}{3}q-\frac{15}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{3}{10}p+\frac{5}{3}q-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-06 18:13:43
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