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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-8}{20}+x)(\frac{-11}{2}-x)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{-x}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{11}{2}x+\frac{2}{5}x+\frac{2}{5}.\frac{11}{2}& \text{Uitwerken } \\ & =-x^2+((\frac{-11}{2})+\frac{2}{5})x+(\frac{-22}{10}) & \text{Neem samen} \\ &=-x^2-\frac{51}{10}x+(\frac{-22}{10}) & \text{Maak de som} \\ &=-x^2-\frac{51}{10}x+(\frac{-11}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-8}{13}-a)(a+\frac{4}{12})& =(\color{red}{-a}+\color{orange}{\frac{-8}{13}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-8}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{13})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{1}{3}a-\frac{8}{13}a-\frac{8}{13}.\frac{1}{3}& \text{Uitwerken } \\ & =-a^2+((\frac{-1}{3})+(\frac{-8}{13}))a-\frac{8}{39} & \text{Neem samen} \\ &=-a^2-\frac{37}{39}a-\frac{8}{39} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(a-(-16))(\frac{-19}{2}+q)& =(\color{red}{a}+\color{orange}{16}).(\color{green}{q}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(16)} . \color{green}{(q)} + \color{orange}{(16)} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{2}a+16q-16.\frac{19}{2}& \text{Uitwerken } \\ & =aq-\frac{19}{2}a+16q-\frac{304}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{19}{2}a+16q-152 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{2}{2}+q)(x-\frac{-3}{19})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{19}q+1x+1.\frac{3}{19}& \text{Uitwerken } \\ & =qx+\frac{3}{19}q+1x+\frac{3}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-\frac{2}{3})(\frac{-1}{19}+p)& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{19}q-\frac{2}{3}p+\frac{2}{3}.\frac{1}{19}& \text{Uitwerken } \\ & =pq-\frac{1}{19}q-\frac{2}{3}p+\frac{2}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{12}-x)(a+\frac{-14}{6})& =(\color{red}{-x}+\color{orange}{\frac{-7}{12}}).(\color{green}{a}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{3}x-\frac{7}{12}a+\frac{7}{12}.\frac{7}{3}& \text{Uitwerken } \\ & =-ax+\frac{7}{3}x-\frac{7}{12}a+\frac{49}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+\frac{19}{3})(\frac{-17}{9}+a)& =(\color{red}{b}+\color{orange}{\frac{19}{3}}).(\color{green}{a}+\color{blue}{\frac{-17}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{9})} + \color{orange}{(\frac{19}{3})} . \color{green}{(a)} + \color{orange}{(\frac{19}{3})} . \color{blue}{(\frac{-17}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{17}{9}b+\frac{19}{3}a-\frac{19}{3}.\frac{17}{9}& \text{Uitwerken } \\ & =ab-\frac{17}{9}b+\frac{19}{3}a-\frac{323}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{4}{16})(q-\frac{-5}{5})& =(\color{red}{p}+\color{orange}{\frac{1}{4}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1p+\frac{1}{4}q+\frac{1}{4}.1& \text{Uitwerken } \\ & =pq+1p+\frac{1}{4}q+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{3}{14})(a+\frac{18}{20})& =(\color{red}{q}+\color{orange}{\frac{3}{14}}).(\color{green}{a}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{3}{14})} . \color{green}{(a)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{10}q+\frac{3}{14}a+\frac{3}{14}.\frac{9}{10}& \text{Uitwerken } \\ & =aq+\frac{9}{10}q+\frac{3}{14}a+\frac{27}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{8}{11})(\frac{14}{3}+p)& =(\color{red}{p}+\color{orange}{\frac{8}{11}}).(\color{green}{p}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{8}{11})} . \color{green}{(p)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{14}{3}p+\frac{8}{11}p+\frac{8}{11}.\frac{14}{3}& \text{Uitwerken } \\ & =p^2+(\frac{14}{3}+\frac{8}{11})p+\frac{112}{33} & \text{Neem samen} \\ &=p^2+\frac{178}{33}p+\frac{112}{33} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(p-\frac{5}{8})(p+\frac{-13}{16})& =(\color{red}{p}+\color{orange}{\frac{-5}{8}}).(\color{green}{p}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{13}{16}p-\frac{5}{8}p+\frac{5}{8}.\frac{13}{16}& \text{Uitwerken } \\ & =p^2+((\frac{-13}{16})+(\frac{-5}{8}))p+\frac{65}{128} & \text{Neem samen} \\ &=p^2-\frac{23}{16}p+\frac{65}{128} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-1}{2}-p)(x-\frac{-10}{2})& =(\color{red}{-p}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(5)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -px-5p-\frac{1}{2}x-\frac{1}{2}.5& \text{Uitwerken } \\ & =-px-5p-\frac{1}{2}x-\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-16 10:43:04
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