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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{19}{4}-q)(\frac{-3}{19}-x)& =(\color{red}{-q}+\color{orange}{\frac{19}{4}}).(\color{green}{-x}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{19}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{19}q-\frac{19}{4}x-\frac{19}{4}.\frac{3}{19}& \text{Uitwerken } \\ & =qx+\frac{3}{19}q-\frac{19}{4}x-\frac{57}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{3}{19}q-\frac{19}{4}x-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{9}{14})(a+\frac{4}{5})& =(\color{red}{a}+\color{orange}{\frac{-9}{14}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{4}{5}a-\frac{9}{14}a-\frac{9}{14}.\frac{4}{5}& \text{Uitwerken } \\ & =a^2+(\frac{4}{5}+(\frac{-9}{14}))a-(\frac{-36}{70}) & \text{Neem samen} \\ &=a^2+\frac{11}{70}a-(\frac{-36}{70}) & \text{Maak de som} \\ &=a^2+\frac{11}{70}a+\frac{18}{35} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(b+\frac{8}{9})(q+\frac{-13}{8})& =(\color{red}{b}+\color{orange}{\frac{8}{9}}).(\color{green}{q}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{8}{9})} . \color{green}{(q)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{8}b+\frac{8}{9}q-\frac{8}{9}.\frac{13}{8}& \text{Uitwerken } \\ & =bq-\frac{13}{8}b+\frac{8}{9}q-\frac{104}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{13}{8}b+\frac{8}{9}q-\frac{13}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{15}{17}-b)(\frac{4}{8}-q)& =(\color{red}{-b}+\color{orange}{\frac{15}{17}}).(\color{green}{-q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{15}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{2}b-\frac{15}{17}q+\frac{15}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =bq-\frac{1}{2}b-\frac{15}{17}q+\frac{15}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{15}+q)(q-\frac{12}{14})& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{6}{7}q-\frac{2}{3}q+\frac{2}{3}.\frac{6}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-6}{7})+(\frac{-2}{3}))q+\frac{12}{21} & \text{Neem samen} \\ &=q^2-\frac{32}{21}q+\frac{12}{21} & \text{Maak de som} \\ &=q^2-\frac{32}{21}q+\frac{4}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-16}{17})(a+\frac{4}{9})& =(\color{red}{q}+\color{orange}{\frac{-16}{17}}).(\color{green}{a}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{9}q-\frac{16}{17}a-\frac{16}{17}.\frac{4}{9}& \text{Uitwerken } \\ & =aq+\frac{4}{9}q-\frac{16}{17}a-\frac{64}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{5}{8}-x)(\frac{18}{13}-b)& =(\color{red}{-x}+\color{orange}{\frac{5}{8}}).(\color{green}{-b}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{5}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{18}{13}x-\frac{5}{8}b+\frac{5}{8}.\frac{18}{13}& \text{Uitwerken } \\ & =bx-\frac{18}{13}x-\frac{5}{8}b+\frac{90}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{18}{13}x-\frac{5}{8}b+\frac{45}{52} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-11}{8}-a)(a+\frac{-12}{2})& =(\color{red}{-a}+\color{orange}{\frac{-11}{8}}).(\color{green}{a}+\color{blue}{(-6)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(-6)} + \color{orange}{(\frac{-11}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -aa+6a-\frac{11}{8}a+\frac{11}{8}.6& \text{Uitwerken } \\ & =-a^2+(6+(\frac{-11}{8}))a+(\frac{-66}{8}) & \text{Neem samen} \\ &=-a^2+\frac{37}{8}a+(\frac{-66}{8}) & \text{Maak de som} \\ &=-a^2+\frac{37}{8}a+(\frac{-33}{4}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-8}{13})(\frac{9}{11}-b)& =(\color{red}{b}+\color{orange}{\frac{8}{13}}).(\color{green}{-b}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{8}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{9}{11}b-\frac{8}{13}b+\frac{8}{13}.\frac{9}{11}& \text{Uitwerken } \\ & =-b^2+(\frac{9}{11}+(\frac{-8}{13}))b+(\frac{-72}{143}) & \text{Neem samen} \\ &=-b^2+\frac{29}{143}b+(\frac{-72}{143}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(19+x)(\frac{-4}{13}-b)& =(\color{red}{x}+\color{orange}{19}).(\color{green}{-b}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(19)} . \color{green}{(-b)} + \color{orange}{(19)} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{13}x-19b-19.\frac{4}{13}& \text{Uitwerken } \\ & =-bx-\frac{4}{13}x-19b-\frac{76}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{1}{20})(b+\frac{-6}{14})& =(\color{red}{b}+\color{orange}{\frac{1}{20}}).(\color{green}{b}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{1}{20})} . \color{green}{(b)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{7}b+\frac{1}{20}b-\frac{1}{20}.\frac{3}{7}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{7})+\frac{1}{20})b-(\frac{-3}{140}) & \text{Neem samen} \\ &=b^2-\frac{53}{140}b-(\frac{-3}{140}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-14}{20})(\frac{12}{17}+q)& =(\color{red}{x}+\color{orange}{\frac{-7}{10}}).(\color{green}{q}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{17}x-\frac{7}{10}q-\frac{7}{10}.\frac{12}{17}& \text{Uitwerken } \\ & =qx+\frac{12}{17}x-\frac{7}{10}q-\frac{84}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{17}x-\frac{7}{10}q-\frac{42}{85} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-04 09:17:11
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