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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{-15}{17})(\frac{17}{18}-b)& =(\color{red}{b}+\color{orange}{\frac{15}{17}}).(\color{green}{-b}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{15}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{17}{18}b-\frac{15}{17}b+\frac{15}{17}.\frac{17}{18}& \text{Uitwerken } \\ & =-b^2+(\frac{17}{18}+(\frac{-15}{17}))b+(\frac{-255}{306}) & \text{Neem samen} \\ &=-b^2+\frac{19}{306}b+(\frac{-255}{306}) & \text{Maak de som} \\ &=-b^2+\frac{19}{306}b+(\frac{-5}{6}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-18}{9}+a)(x-\frac{-17}{15})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{15}a-2x-2.\frac{17}{15}& \text{Uitwerken } \\ & =ax+\frac{17}{15}a-2x-\frac{34}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{11}{13})(\frac{20}{5}-q)& =(\color{red}{p}+\color{orange}{\frac{11}{13}}).(\color{green}{-q}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{11}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -pq+4p-\frac{11}{13}q+\frac{11}{13}.4& \text{Uitwerken } \\ & =-pq+4p-\frac{11}{13}q+\frac{44}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-16}{4})(a-\frac{-8}{16})& =(\color{red}{q}+\color{orange}{4}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{2}q+4a+4.\frac{1}{2}& \text{Uitwerken } \\ & =aq+\frac{1}{2}q+4a+\frac{4}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{1}{2}q+4a+2 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x-\frac{20}{18})(a+\frac{6}{13})& =(\color{red}{x}+\color{orange}{\frac{-10}{9}}).(\color{green}{a}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{6}{13}x-\frac{10}{9}a-\frac{10}{9}.\frac{6}{13}& \text{Uitwerken } \\ & =ax+\frac{6}{13}x-\frac{10}{9}a-\frac{60}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{6}{13}x-\frac{10}{9}a-\frac{20}{39} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-19}{6})(\frac{14}{2}+x)& =(\color{red}{a}+\color{orange}{\frac{-19}{6}}).(\color{green}{x}+\color{blue}{7})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(7)} + \color{orange}{(\frac{-19}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = ax+7a-\frac{19}{6}x-\frac{19}{6}.7& \text{Uitwerken } \\ & =ax+7a-\frac{19}{6}x-\frac{133}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-9}{15})(\frac{19}{20}-b)& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{-b}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{19}{20}q-\frac{3}{5}b+\frac{3}{5}.\frac{19}{20}& \text{Uitwerken } \\ & =-bq+\frac{19}{20}q-\frac{3}{5}b+\frac{57}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-9}{10})(\frac{-1}{11}+x)& =(\color{red}{q}+\color{orange}{\frac{-9}{10}}).(\color{green}{x}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{11}q-\frac{9}{10}x+\frac{9}{10}.\frac{1}{11}& \text{Uitwerken } \\ & =qx-\frac{1}{11}q-\frac{9}{10}x+\frac{9}{110} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-15}{4}-b)(\frac{9}{11}-b)& =(\color{red}{-b}+\color{orange}{\frac{-15}{4}}).(\color{green}{-b}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{9}{11}b+\frac{15}{4}b-\frac{15}{4}.\frac{9}{11}& \text{Uitwerken } \\ & =b^2+((\frac{-9}{11})+\frac{15}{4})b-(\frac{-135}{44}) & \text{Neem samen} \\ &=b^2+\frac{129}{44}b-(\frac{-135}{44}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p+\frac{3}{2})(\frac{-20}{15}-b)& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{-b}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{3}p-\frac{3}{2}b-\frac{3}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =-bp-\frac{4}{3}p-\frac{3}{2}b-\frac{12}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{4}{3}p-\frac{3}{2}b-2 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-11}{18})(q-\frac{8}{14})& =(\color{red}{x}+\color{orange}{\frac{-11}{18}}).(\color{green}{q}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{7}x-\frac{11}{18}q+\frac{11}{18}.\frac{4}{7}& \text{Uitwerken } \\ & =qx-\frac{4}{7}x-\frac{11}{18}q+\frac{44}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{4}{7}x-\frac{11}{18}q+\frac{22}{63} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-5}{7}-a)(a+\frac{-5}{14})& =(\color{red}{-a}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{5}{14}a-\frac{5}{7}a+\frac{5}{7}.\frac{5}{14}& \text{Uitwerken } \\ & =-a^2+(\frac{5}{14}+(\frac{-5}{7}))a+(\frac{-25}{98}) & \text{Neem samen} \\ &=-a^2-\frac{5}{14}a+(\frac{-25}{98}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-03 05:46:21
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