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

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Werk uit en vereenvoudig

  1. \((\frac{14}{6}-p)(\frac{-6}{9}+b)\)
  2. \((p-\frac{-11}{18})(p-\frac{10}{2})\)
  3. \((p+\frac{-8}{18})(q+\frac{-16}{16})\)
  4. \((x-\frac{-17}{17})(\frac{-20}{13}+q)\)
  5. \((x-\frac{-15}{6})(\frac{4}{20}-x)\)
  6. \((\frac{-9}{7}-x)(q-\frac{-9}{5})\)
  7. \(((-20)-p)(\frac{17}{8}+a)\)
  8. \((p-\frac{1}{20})(q+\frac{-18}{19})\)
  9. \((b+\frac{-5}{13})(p-\frac{-19}{18})\)
  10. \((p-18)(a-\frac{-2}{13})\)
  11. \((q+\frac{1}{13})(\frac{4}{17}-q)\)
  12. \((p-\frac{-11}{13})(q-\frac{13}{16})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{14}{6}-p)(\frac{-6}{9}+b)& =(\color{red}{-p}+\color{orange}{\frac{7}{3}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{7}{3})} . \color{green}{(b)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{2}{3}p+\frac{7}{3}b-\frac{7}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-bp+\frac{2}{3}p+\frac{7}{3}b-\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-11}{18})(p-\frac{10}{2})& =(\color{red}{p}+\color{orange}{\frac{11}{18}}).(\color{green}{p}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(\frac{11}{18})} . \color{green}{(p)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = pp-5p+\frac{11}{18}p-\frac{11}{18}.5& \text{Uitwerken } \\ & =p^2+((-5)+\frac{11}{18})p-(\frac{-55}{18}) & \text{Neem samen} \\ &=p^2-\frac{79}{18}p-(\frac{-55}{18}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-8}{18})(q+\frac{-16}{16})& =(\color{red}{p}+\color{orange}{\frac{-4}{9}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-4}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1p-\frac{4}{9}q+\frac{4}{9}.1& \text{Uitwerken } \\ & =pq-1p-\frac{4}{9}q+\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-17}{17})(\frac{-20}{13}+q)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{20}{13}x+1q-1.\frac{20}{13}& \text{Uitwerken } \\ & =qx-\frac{20}{13}x+1q-\frac{20}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{-15}{6})(\frac{4}{20}-x)& =(\color{red}{x}+\color{orange}{\frac{5}{2}}).(\color{green}{-x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{5}x-\frac{5}{2}x+\frac{5}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{5}+(\frac{-5}{2}))x+(\frac{-5}{10}) & \text{Neem samen} \\ &=-x^2-\frac{23}{10}x+(\frac{-5}{10}) & \text{Maak de som} \\ &=-x^2-\frac{23}{10}x+(\frac{-1}{2}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{7}-x)(q-\frac{-9}{5})& =(\color{red}{-x}+\color{orange}{\frac{-9}{7}}).(\color{green}{q}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{9}{5}x-\frac{9}{7}q-\frac{9}{7}.\frac{9}{5}& \text{Uitwerken } \\ & =-qx-\frac{9}{5}x-\frac{9}{7}q-\frac{81}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}((-20)-p)(\frac{17}{8}+a)& =(\color{red}{-p}+\color{orange}{(-20)}).(\color{green}{a}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(-20)} . \color{green}{(a)} + \color{orange}{(-20)} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{8}p-20a-20.\frac{17}{8}& \text{Uitwerken } \\ & =-ap-\frac{17}{8}p-20a-\frac{340}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{17}{8}p-20a-\frac{85}{2} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p-\frac{1}{20})(q+\frac{-18}{19})& =(\color{red}{p}+\color{orange}{\frac{-1}{20}}).(\color{green}{q}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{-1}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{18}{19}p-\frac{1}{20}q+\frac{1}{20}.\frac{18}{19}& \text{Uitwerken } \\ & =pq-\frac{18}{19}p-\frac{1}{20}q+\frac{18}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{18}{19}p-\frac{1}{20}q+\frac{9}{190} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-5}{13})(p-\frac{-19}{18})& =(\color{red}{b}+\color{orange}{\frac{-5}{13}}).(\color{green}{p}+\color{blue}{\frac{19}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{18})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{19}{18})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{18}b-\frac{5}{13}p-\frac{5}{13}.\frac{19}{18}& \text{Uitwerken } \\ & =bp+\frac{19}{18}b-\frac{5}{13}p-\frac{95}{234} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-18)(a-\frac{-2}{13})& =(\color{red}{p}+\color{orange}{(-18)}).(\color{green}{a}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(-18)} . \color{green}{(a)} + \color{orange}{(-18)} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{13}p-18a-18.\frac{2}{13}& \text{Uitwerken } \\ & =ap+\frac{2}{13}p-18a-\frac{36}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{1}{13})(\frac{4}{17}-q)& =(\color{red}{q}+\color{orange}{\frac{1}{13}}).(\color{green}{-q}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{1}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{4}{17}q-\frac{1}{13}q+\frac{1}{13}.\frac{4}{17}& \text{Uitwerken } \\ & =-q^2+(\frac{4}{17}+(\frac{-1}{13}))q+(\frac{-4}{221}) & \text{Neem samen} \\ &=-q^2+\frac{35}{221}q+(\frac{-4}{221}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-11}{13})(q-\frac{13}{16})& =(\color{red}{p}+\color{orange}{\frac{11}{13}}).(\color{green}{q}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{11}{13})} . \color{green}{(q)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{16}p+\frac{11}{13}q-\frac{11}{13}.\frac{13}{16}& \text{Uitwerken } \\ & =pq-\frac{13}{16}p+\frac{11}{13}q-\frac{143}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{13}{16}p+\frac{11}{13}q-\frac{11}{16} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-11 18:28:32
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