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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{6}{17})(a+\frac{15}{10})& =(\color{red}{a}+\color{orange}{\frac{6}{17}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{6}{17})} . \color{green}{(a)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{2}a+\frac{6}{17}a+\frac{6}{17}.\frac{3}{2}& \text{Uitwerken } \\ & =a^2+(\frac{3}{2}+\frac{6}{17})a+\frac{18}{34} & \text{Neem samen} \\ &=a^2+\frac{63}{34}a+\frac{18}{34} & \text{Maak de som} \\ &=a^2+\frac{63}{34}a+\frac{9}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(5-q)(\frac{-17}{14}+q)& =(\color{red}{-q}+\color{orange}{5}).(\color{green}{q}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(5)} . \color{green}{(q)} + \color{orange}{(5)} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{17}{14}q+5q-5.\frac{17}{14}& \text{Uitwerken } \\ & =-q^2+(\frac{17}{14}+5)q-\frac{85}{14} & \text{Neem samen} \\ &=-q^2+\frac{87}{14}q-\frac{85}{14} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-19}{5}+b)(q+\frac{-15}{8})& =(\color{red}{b}+\color{orange}{\frac{-19}{5}}).(\color{green}{q}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{15}{8}b-\frac{19}{5}q+\frac{19}{5}.\frac{15}{8}& \text{Uitwerken } \\ & =bq-\frac{15}{8}b-\frac{19}{5}q+\frac{285}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{15}{8}b-\frac{19}{5}q+\frac{57}{8} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q+\frac{7}{17})(b+\frac{-13}{3})& =(\color{red}{q}+\color{orange}{\frac{7}{17}}).(\color{green}{b}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{7}{17})} . \color{green}{(b)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{3}q+\frac{7}{17}b-\frac{7}{17}.\frac{13}{3}& \text{Uitwerken } \\ & =bq-\frac{13}{3}q+\frac{7}{17}b-\frac{91}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-17}{2}+b)(\frac{7}{8}+x)& =(\color{red}{b}+\color{orange}{\frac{-17}{2}}).(\color{green}{x}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-17}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{2})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{8}b-\frac{17}{2}x-\frac{17}{2}.\frac{7}{8}& \text{Uitwerken } \\ & =bx+\frac{7}{8}b-\frac{17}{2}x-\frac{119}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}((-4)-a)(\frac{8}{2}+q)& =(\color{red}{-a}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(4)} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -aq-4a-4q-4.4& \text{Uitwerken } \\ & =-aq-4a-4q-16 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{6}{14}-q)(a+\frac{12}{19})& =(\color{red}{-q}+\color{orange}{\frac{3}{7}}).(\color{green}{a}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{12}{19}q+\frac{3}{7}a+\frac{3}{7}.\frac{12}{19}& \text{Uitwerken } \\ & =-aq-\frac{12}{19}q+\frac{3}{7}a+\frac{36}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{8}{13})(p-\frac{17}{10})& =(\color{red}{p}+\color{orange}{\frac{8}{13}}).(\color{green}{p}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{8}{13})} . \color{green}{(p)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{10}p+\frac{8}{13}p-\frac{8}{13}.\frac{17}{10}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{10})+\frac{8}{13})p-(\frac{-136}{130}) & \text{Neem samen} \\ &=p^2-\frac{141}{130}p-(\frac{-136}{130}) & \text{Maak de som} \\ &=p^2-\frac{141}{130}p+\frac{68}{65} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{13}{4}-q)(\frac{-15}{12}+x)& =(\color{red}{-q}+\color{orange}{\frac{13}{4}}).(\color{green}{x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{13}{4})} . \color{green}{(x)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{4}q+\frac{13}{4}x-\frac{13}{4}.\frac{5}{4}& \text{Uitwerken } \\ & =-qx+\frac{5}{4}q+\frac{13}{4}x-\frac{65}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{15}{17})(\frac{20}{7}+b)& =(\color{red}{q}+\color{orange}{\frac{15}{17}}).(\color{green}{b}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{15}{17})} . \color{green}{(b)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{20}{7}q+\frac{15}{17}b+\frac{15}{17}.\frac{20}{7}& \text{Uitwerken } \\ & =bq+\frac{20}{7}q+\frac{15}{17}b+\frac{300}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-4}{7})(\frac{-10}{2}+p)& =(\color{red}{b}+\color{orange}{\frac{-4}{7}}).(\color{green}{p}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-5)} + \color{orange}{(\frac{-4}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = bp-5b-\frac{4}{7}p+\frac{4}{7}.5& \text{Uitwerken } \\ & =bp-5b-\frac{4}{7}p+\frac{20}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{9}-b)(\frac{-4}{6}+q)& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{3}b-2q+2.\frac{2}{3}& \text{Uitwerken } \\ & =-bq+\frac{2}{3}b-2q+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-04 19:18:58
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