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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{19}{20}+q)(\frac{-19}{12}-q)& =(\color{red}{q}+\color{orange}{\frac{19}{20}}).(\color{green}{-q}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{19}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{19}{12}q-\frac{19}{20}q-\frac{19}{20}.\frac{19}{12}& \text{Uitwerken } \\ & =-q^2+((\frac{-19}{12})+(\frac{-19}{20}))q-\frac{361}{240} & \text{Neem samen} \\ &=-q^2-\frac{152}{60}q-\frac{361}{240} & \text{Maak de som} \\ &=-q^2-\frac{38}{15}q-\frac{361}{240} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-10}{4})(\frac{13}{11}-p)& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{-p}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{11}b+\frac{5}{2}p-\frac{5}{2}.\frac{13}{11}& \text{Uitwerken } \\ & =-bp+\frac{13}{11}b+\frac{5}{2}p-\frac{65}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{1}{20}+x)(q+\frac{20}{3})& =(\color{red}{x}+\color{orange}{\frac{1}{20}}).(\color{green}{q}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{1}{20})} . \color{green}{(q)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{20}{3}x+\frac{1}{20}q+\frac{1}{20}.\frac{20}{3}& \text{Uitwerken } \\ & =qx+\frac{20}{3}x+\frac{1}{20}q+\frac{20}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{20}{3}x+\frac{1}{20}q+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-6}{17})((-15)+x)& =(\color{red}{q}+\color{orange}{\frac{6}{17}}).(\color{green}{x}+\color{blue}{(-15)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-15)} + \color{orange}{(\frac{6}{17})} . \color{green}{(x)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = qx-15q+\frac{6}{17}x-\frac{6}{17}.15& \text{Uitwerken } \\ & =qx-15q+\frac{6}{17}x-\frac{90}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-\frac{14}{6})(\frac{20}{3}+b)& =(\color{red}{q}+\color{orange}{\frac{-7}{3}}).(\color{green}{b}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{20}{3}q-\frac{7}{3}b-\frac{7}{3}.\frac{20}{3}& \text{Uitwerken } \\ & =bq+\frac{20}{3}q-\frac{7}{3}b-\frac{140}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-19}{6})(\frac{17}{16}+a)& =(\color{red}{x}+\color{orange}{\frac{-19}{6}}).(\color{green}{a}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{16}x-\frac{19}{6}a-\frac{19}{6}.\frac{17}{16}& \text{Uitwerken } \\ & =ax+\frac{17}{16}x-\frac{19}{6}a-\frac{323}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{16}{18})(\frac{16}{14}+a)& =(\color{red}{a}+\color{orange}{\frac{-8}{9}}).(\color{green}{a}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{8}{7}a-\frac{8}{9}a-\frac{8}{9}.\frac{8}{7}& \text{Uitwerken } \\ & =a^2+(\frac{8}{7}+(\frac{-8}{9}))a-(\frac{-64}{63}) & \text{Neem samen} \\ &=a^2+\frac{16}{63}a-(\frac{-64}{63}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{2}{13}+q)(\frac{-4}{19}-p)& =(\color{red}{q}+\color{orange}{\frac{2}{13}}).(\color{green}{-p}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{2}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{4}{19}q-\frac{2}{13}p-\frac{2}{13}.\frac{4}{19}& \text{Uitwerken } \\ & =-pq-\frac{4}{19}q-\frac{2}{13}p-\frac{8}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{5}+a)(\frac{17}{15}-b)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{17}{15}a-1b+1.\frac{17}{15}& \text{Uitwerken } \\ & =-ab+\frac{17}{15}a-1b+\frac{17}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-2}{20}-q)(a+\frac{-20}{3})& =(\color{red}{-q}+\color{orange}{\frac{-1}{10}}).(\color{green}{a}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{20}{3}q-\frac{1}{10}a+\frac{1}{10}.\frac{20}{3}& \text{Uitwerken } \\ & =-aq+\frac{20}{3}q-\frac{1}{10}a+\frac{20}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{20}{3}q-\frac{1}{10}a+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-7}{5}+p)(\frac{14}{13}+x)& =(\color{red}{p}+\color{orange}{\frac{-7}{5}}).(\color{green}{x}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{14}{13}p-\frac{7}{5}x-\frac{7}{5}.\frac{14}{13}& \text{Uitwerken } \\ & =px+\frac{14}{13}p-\frac{7}{5}x-\frac{98}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{20}{14}-p)(\frac{17}{20}-x)& =(\color{red}{-p}+\color{orange}{\frac{10}{7}}).(\color{green}{-x}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{10}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{20}p-\frac{10}{7}x+\frac{10}{7}.\frac{17}{20}& \text{Uitwerken } \\ & =px-\frac{17}{20}p-\frac{10}{7}x+\frac{170}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{17}{20}p-\frac{10}{7}x+\frac{17}{14} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-16 13:11:41
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