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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{19}{11}+q)(p+\frac{-9}{12})& =(\color{red}{q}+\color{orange}{\frac{19}{11}}).(\color{green}{p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{19}{11})} . \color{green}{(p)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{4}q+\frac{19}{11}p-\frac{19}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =pq-\frac{3}{4}q+\frac{19}{11}p-\frac{57}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-5}{13}+q)(\frac{18}{8}+b)& =(\color{red}{q}+\color{orange}{\frac{-5}{13}}).(\color{green}{b}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{4}q-\frac{5}{13}b-\frac{5}{13}.\frac{9}{4}& \text{Uitwerken } \\ & =bq+\frac{9}{4}q-\frac{5}{13}b-\frac{45}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{12}{12}-q)(\frac{-8}{13}-a)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{13}q-1a-1.\frac{8}{13}& \text{Uitwerken } \\ & =aq+\frac{8}{13}q-1a-\frac{8}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-3}{16}-p)(\frac{14}{11}+p)& =(\color{red}{-p}+\color{orange}{\frac{-3}{16}}).(\color{green}{p}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{14}{11}p-\frac{3}{16}p-\frac{3}{16}.\frac{14}{11}& \text{Uitwerken } \\ & =-p^2+((\frac{-14}{11})+(\frac{-3}{16}))p-\frac{42}{176} & \text{Neem samen} \\ &=-p^2-\frac{257}{176}p-\frac{42}{176} & \text{Maak de som} \\ &=-p^2-\frac{257}{176}p-\frac{21}{88} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{6}+p)(\frac{-2}{19}+a)& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{a}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{19}p-\frac{5}{3}a+\frac{5}{3}.\frac{2}{19}& \text{Uitwerken } \\ & =ap-\frac{2}{19}p-\frac{5}{3}a+\frac{10}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-3}{15})(p-\frac{-4}{17})& =(\color{red}{p}+\color{orange}{\frac{1}{5}}).(\color{green}{p}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{4}{17}p+\frac{1}{5}p+\frac{1}{5}.\frac{4}{17}& \text{Uitwerken } \\ & =p^2+(\frac{4}{17}+\frac{1}{5})p+\frac{4}{85} & \text{Neem samen} \\ &=p^2+\frac{37}{85}p+\frac{4}{85} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-10}{20})(\frac{-10}{11}+q)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{10}{11}q+\frac{1}{2}q-\frac{1}{2}.\frac{10}{11}& \text{Uitwerken } \\ & =q^2+((\frac{-10}{11})+\frac{1}{2})q-(\frac{-10}{22}) & \text{Neem samen} \\ &=q^2-\frac{9}{22}q-(\frac{-10}{22}) & \text{Maak de som} \\ &=q^2-\frac{9}{22}q+\frac{5}{11} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{16}+x)(\frac{18}{5}-b)& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{-b}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{18}{5}x-\frac{1}{4}b+\frac{1}{4}.\frac{18}{5}& \text{Uitwerken } \\ & =-bx+\frac{18}{5}x-\frac{1}{4}b+\frac{18}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{18}{5}x-\frac{1}{4}b+\frac{9}{10} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-1}{9}-p)(a-\frac{-13}{7})& =(\color{red}{-p}+\color{orange}{\frac{-1}{9}}).(\color{green}{a}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{7}p-\frac{1}{9}a-\frac{1}{9}.\frac{13}{7}& \text{Uitwerken } \\ & =-ap-\frac{13}{7}p-\frac{1}{9}a-\frac{13}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-17}{12}+p)(p-\frac{1}{10})& =(\color{red}{p}+\color{orange}{\frac{-17}{12}}).(\color{green}{p}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{10}p-\frac{17}{12}p+\frac{17}{12}.\frac{1}{10}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{10})+(\frac{-17}{12}))p+\frac{17}{120} & \text{Neem samen} \\ &=p^2-\frac{91}{60}p+\frac{17}{120} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a+\frac{-18}{16})(\frac{-10}{2}+q)& =(\color{red}{a}+\color{orange}{\frac{-9}{8}}).(\color{green}{q}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-5)} + \color{orange}{(\frac{-9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = aq-5a-\frac{9}{8}q+\frac{9}{8}.5& \text{Uitwerken } \\ & =aq-5a-\frac{9}{8}q+\frac{45}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-8}{18})(\frac{-14}{12}+a)& =(\color{red}{b}+\color{orange}{\frac{-4}{9}}).(\color{green}{a}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{6}b-\frac{4}{9}a+\frac{4}{9}.\frac{7}{6}& \text{Uitwerken } \\ & =ab-\frac{7}{6}b-\frac{4}{9}a+\frac{28}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{7}{6}b-\frac{4}{9}a+\frac{14}{27} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-09-19 09:02:41
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