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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{7}{8}+p)(p-\frac{-10}{9})& =(\color{red}{p}+\color{orange}{\frac{7}{8}}).(\color{green}{p}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{10}{9}p+\frac{7}{8}p+\frac{7}{8}.\frac{10}{9}& \text{Uitwerken } \\ & =p^2+(\frac{10}{9}+\frac{7}{8})p+\frac{70}{72} & \text{Neem samen} \\ &=p^2+\frac{143}{72}p+\frac{70}{72} & \text{Maak de som} \\ &=p^2+\frac{143}{72}p+\frac{35}{36} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-18}{5})(\frac{4}{5}+b)& =(\color{red}{a}+\color{orange}{\frac{-18}{5}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{4}{5}a-\frac{18}{5}b-\frac{18}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =ab+\frac{4}{5}a-\frac{18}{5}b-\frac{72}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{2}{6})(q+\frac{7}{5})& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{5}q-\frac{1}{3}q-\frac{1}{3}.\frac{7}{5}& \text{Uitwerken } \\ & =q^2+(\frac{7}{5}+(\frac{-1}{3}))q-(\frac{-7}{15}) & \text{Neem samen} \\ &=q^2+\frac{16}{15}q-(\frac{-7}{15}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-6}{5}-q)(\frac{2}{4}-x)& =(\color{red}{-q}+\color{orange}{\frac{-6}{5}}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{2}q+\frac{6}{5}x-\frac{6}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =qx-\frac{1}{2}q+\frac{6}{5}x-\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{2}q+\frac{6}{5}x-\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}((-5)-a)(q+\frac{2}{20})& =(\color{red}{-a}+\color{orange}{(-5)}).(\color{green}{q}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(-5)} . \color{green}{(q)} + \color{orange}{(-5)} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{10}a-5q-5.\frac{1}{10}& \text{Uitwerken } \\ & =-aq-\frac{1}{10}a-5q-\frac{5}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{1}{10}a-5q-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{11}-x)(\frac{-16}{11}+p)& =(\color{red}{-x}+\color{orange}{\frac{-9}{11}}).(\color{green}{p}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{16}{11}x-\frac{9}{11}p+\frac{9}{11}.\frac{16}{11}& \text{Uitwerken } \\ & =-px+\frac{16}{11}x-\frac{9}{11}p+\frac{144}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+1)(\frac{-2}{15}+a)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-2}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{15})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-2}{15})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{15}b+1a-1.\frac{2}{15}& \text{Uitwerken } \\ & =ab-\frac{2}{15}b+1a-\frac{2}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{1}{15})(\frac{-3}{12}-q)& =(\color{red}{a}+\color{orange}{\frac{-1}{15}}).(\color{green}{-q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{4}a+\frac{1}{15}q+\frac{1}{15}.\frac{1}{4}& \text{Uitwerken } \\ & =-aq-\frac{1}{4}a+\frac{1}{15}q+\frac{1}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-9}{19}-x)(x+\frac{-11}{6})& =(\color{red}{-x}+\color{orange}{\frac{-9}{19}}).(\color{green}{x}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{11}{6}x-\frac{9}{19}x+\frac{9}{19}.\frac{11}{6}& \text{Uitwerken } \\ & =-x^2+(\frac{11}{6}+(\frac{-9}{19}))x+(\frac{-99}{114}) & \text{Neem samen} \\ &=-x^2+\frac{155}{114}x+(\frac{-99}{114}) & \text{Maak de som} \\ &=-x^2+\frac{155}{114}x+(\frac{-33}{38}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-17}{3}-q)(\frac{-4}{11}+q)& =(\color{red}{-q}+\color{orange}{\frac{-17}{3}}).(\color{green}{q}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{4}{11}q-\frac{17}{3}q+\frac{17}{3}.\frac{4}{11}& \text{Uitwerken } \\ & =-q^2+(\frac{4}{11}+(\frac{-17}{3}))q+(\frac{-68}{33}) & \text{Neem samen} \\ &=-q^2-\frac{175}{33}q+(\frac{-68}{33}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-4}{16}-a)(\frac{-17}{18}-b)& =(\color{red}{-a}+\color{orange}{\frac{-1}{4}}).(\color{green}{-b}+\color{blue}{\frac{-17}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{18})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-17}{18})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{18}a+\frac{1}{4}b+\frac{1}{4}.\frac{17}{18}& \text{Uitwerken } \\ & =ab+\frac{17}{18}a+\frac{1}{4}b+\frac{17}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{14}-b)(q-\frac{3}{5})& =(\color{red}{-b}+\color{orange}{\frac{13}{14}}).(\color{green}{q}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{13}{14})} . \color{green}{(q)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{5}b+\frac{13}{14}q-\frac{13}{14}.\frac{3}{5}& \text{Uitwerken } \\ & =-bq+\frac{3}{5}b+\frac{13}{14}q-\frac{39}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-19 04:47:27
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