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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-8}{5})(\frac{-19}{13}-a)& =(\color{red}{q}+\color{orange}{\frac{8}{5}}).(\color{green}{-a}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{8}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{13}q-\frac{8}{5}a-\frac{8}{5}.\frac{19}{13}& \text{Uitwerken } \\ & =-aq-\frac{19}{13}q-\frac{8}{5}a-\frac{152}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-10}{9}+x)(\frac{-5}{17}+q)& =(\color{red}{x}+\color{orange}{\frac{-10}{9}}).(\color{green}{q}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{17}x-\frac{10}{9}q+\frac{10}{9}.\frac{5}{17}& \text{Uitwerken } \\ & =qx-\frac{5}{17}x-\frac{10}{9}q+\frac{50}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{18}{15}+a)(\frac{10}{17}+b)& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{b}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(\frac{6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{10}{17}a+\frac{6}{5}b+\frac{6}{5}.\frac{10}{17}& \text{Uitwerken } \\ & =ab+\frac{10}{17}a+\frac{6}{5}b+\frac{60}{85} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{10}{17}a+\frac{6}{5}b+\frac{12}{17} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-7}{7}+p)(\frac{-16}{17}+b)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{16}{17}p-1b+1.\frac{16}{17}& \text{Uitwerken } \\ & =bp-\frac{16}{17}p-1b+\frac{16}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{11}{18})((-12)+x)& =(\color{red}{b}+\color{orange}{\frac{11}{18}}).(\color{green}{x}+\color{blue}{(-12)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-12)} + \color{orange}{(\frac{11}{18})} . \color{green}{(x)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = bx-12b+\frac{11}{18}x-\frac{11}{18}.12& \text{Uitwerken } \\ & =bx-12b+\frac{11}{18}x-\frac{132}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-12b+\frac{11}{18}x-\frac{22}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{18}{11})(\frac{-20}{14}-q)& =(\color{red}{x}+\color{orange}{\frac{18}{11}}).(\color{green}{-q}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{18}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{10}{7}x-\frac{18}{11}q-\frac{18}{11}.\frac{10}{7}& \text{Uitwerken } \\ & =-qx-\frac{10}{7}x-\frac{18}{11}q-\frac{180}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{10}{13}-b)(\frac{-16}{17}-b)& =(\color{red}{-b}+\color{orange}{\frac{10}{13}}).(\color{green}{-b}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{10}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{16}{17}b-\frac{10}{13}b-\frac{10}{13}.\frac{16}{17}& \text{Uitwerken } \\ & =b^2+(\frac{16}{17}+(\frac{-10}{13}))b-(\frac{-160}{221}) & \text{Neem samen} \\ &=b^2+\frac{38}{221}b-(\frac{-160}{221}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(b-\frac{18}{19})(\frac{-8}{19}-q)& =(\color{red}{b}+\color{orange}{\frac{-18}{19}}).(\color{green}{-q}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{8}{19}b+\frac{18}{19}q+\frac{18}{19}.\frac{8}{19}& \text{Uitwerken } \\ & =-bq-\frac{8}{19}b+\frac{18}{19}q+\frac{144}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{7}{4}+a)(a+\frac{-8}{13})& =(\color{red}{a}+\color{orange}{\frac{7}{4}}).(\color{green}{a}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{8}{13}a+\frac{7}{4}a-\frac{7}{4}.\frac{8}{13}& \text{Uitwerken } \\ & =a^2+((\frac{-8}{13})+\frac{7}{4})a-(\frac{-56}{52}) & \text{Neem samen} \\ &=a^2+\frac{59}{52}a-(\frac{-56}{52}) & \text{Maak de som} \\ &=a^2+\frac{59}{52}a+\frac{14}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(q+\frac{18}{20})(q-\frac{-17}{15})& =(\color{red}{q}+\color{orange}{\frac{9}{10}}).(\color{green}{q}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(\frac{9}{10})} . \color{green}{(q)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{17}{15}q+\frac{9}{10}q+\frac{9}{10}.\frac{17}{15}& \text{Uitwerken } \\ & =q^2+(\frac{17}{15}+\frac{9}{10})q+\frac{153}{150} & \text{Neem samen} \\ &=q^2+\frac{61}{30}q+\frac{153}{150} & \text{Maak de som} \\ &=q^2+\frac{61}{30}q+\frac{51}{50} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}((-2)-q)(\frac{9}{12}+p)& =(\color{red}{-q}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{4}q-2p-2.\frac{3}{4}& \text{Uitwerken } \\ & =-pq-\frac{3}{4}q-2p-\frac{6}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{3}{4}q-2p-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{13}-b)(\frac{4}{8}-a)& =(\color{red}{-b}+\color{orange}{\frac{-2}{13}}).(\color{green}{-a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{2}b+\frac{2}{13}a-\frac{2}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =ab-\frac{1}{2}b+\frac{2}{13}a-\frac{2}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{2}b+\frac{2}{13}a-\frac{1}{13} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-18 19:12:36
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