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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{14}-q)(a-\frac{-10}{6})& =(\color{red}{-q}+\color{orange}{\frac{11}{14}}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{11}{14})} . \color{green}{(a)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{3}q+\frac{11}{14}a+\frac{11}{14}.\frac{5}{3}& \text{Uitwerken } \\ & =-aq-\frac{5}{3}q+\frac{11}{14}a+\frac{55}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-11}{2})(\frac{5}{3}-p)& =(\color{red}{b}+\color{orange}{\frac{-11}{2}}).(\color{green}{-p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-11}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{3}b+\frac{11}{2}p-\frac{11}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =-bp+\frac{5}{3}b+\frac{11}{2}p-\frac{55}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{10}{7}+a)(a+\frac{20}{3})& =(\color{red}{a}+\color{orange}{\frac{10}{7}}).(\color{green}{a}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{10}{7})} . \color{green}{(a)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{20}{3}a+\frac{10}{7}a+\frac{10}{7}.\frac{20}{3}& \text{Uitwerken } \\ & =a^2+(\frac{20}{3}+\frac{10}{7})a+\frac{200}{21} & \text{Neem samen} \\ &=a^2+\frac{170}{21}a+\frac{200}{21} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-8}{3})(\frac{-18}{15}+x)& =(\color{red}{q}+\color{orange}{\frac{-8}{3}}).(\color{green}{x}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{6}{5}q-\frac{8}{3}x+\frac{8}{3}.\frac{6}{5}& \text{Uitwerken } \\ & =qx-\frac{6}{5}q-\frac{8}{3}x+\frac{48}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{6}{5}q-\frac{8}{3}x+\frac{16}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-11}{7}-x)(\frac{15}{5}-q)& =(\color{red}{-x}+\color{orange}{\frac{-11}{7}}).(\color{green}{-q}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(3)} + \color{orange}{(\frac{-11}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = qx-3x+\frac{11}{7}q-\frac{11}{7}.3& \text{Uitwerken } \\ & =qx-3x+\frac{11}{7}q-\frac{33}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{8}{14})((-13)-p)& =(\color{red}{a}+\color{orange}{\frac{4}{7}}).(\color{green}{-p}+\color{blue}{(-13)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(-13)} + \color{orange}{(\frac{4}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = -ap-13a-\frac{4}{7}p-\frac{4}{7}.13& \text{Uitwerken } \\ & =-ap-13a-\frac{4}{7}p-\frac{52}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{14}{5})(a-\frac{9}{2})& =(\color{red}{a}+\color{orange}{\frac{-14}{5}}).(\color{green}{a}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{9}{2}a-\frac{14}{5}a+\frac{14}{5}.\frac{9}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-9}{2})+(\frac{-14}{5}))a+\frac{126}{10} & \text{Neem samen} \\ &=a^2-\frac{73}{10}a+\frac{126}{10} & \text{Maak de som} \\ &=a^2-\frac{73}{10}a+\frac{63}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-10}{4}+b)(b-\frac{-19}{4})& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{19}{4}b-\frac{5}{2}b-\frac{5}{2}.\frac{19}{4}& \text{Uitwerken } \\ & =b^2+(\frac{19}{4}+(\frac{-5}{2}))b-(\frac{-95}{8}) & \text{Neem samen} \\ &=b^2+\frac{9}{4}b-(\frac{-95}{8}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{20}+b)(\frac{7}{10}+b)& =(\color{red}{b}+\color{orange}{\frac{-19}{20}}).(\color{green}{b}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{7}{10}b-\frac{19}{20}b-\frac{19}{20}.\frac{7}{10}& \text{Uitwerken } \\ & =b^2+(\frac{7}{10}+(\frac{-19}{20}))b-(\frac{-133}{200}) & \text{Neem samen} \\ &=b^2-\frac{5}{20}b-(\frac{-133}{200}) & \text{Maak de som} \\ &=b^2-\frac{1}{4}b+\frac{133}{200} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(b-\frac{18}{19})(x+(-5))& =(\color{red}{b}+\color{orange}{\frac{-18}{19}}).(\color{green}{x}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-5)} + \color{orange}{(\frac{-18}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = bx-5b-\frac{18}{19}x+\frac{18}{19}.5& \text{Uitwerken } \\ & =bx-5b-\frac{18}{19}x+\frac{90}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{18}-a)(x-\frac{-17}{14})& =(\color{red}{-a}+\color{orange}{\frac{2}{9}}).(\color{green}{x}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{2}{9})} . \color{green}{(x)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{17}{14}a+\frac{2}{9}x+\frac{2}{9}.\frac{17}{14}& \text{Uitwerken } \\ & =-ax-\frac{17}{14}a+\frac{2}{9}x+\frac{34}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{17}{14}a+\frac{2}{9}x+\frac{17}{63} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-\frac{17}{18})(b+\frac{-15}{8})& =(\color{red}{b}+\color{orange}{\frac{-17}{18}}).(\color{green}{b}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{15}{8}b-\frac{17}{18}b+\frac{17}{18}.\frac{15}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-15}{8})+(\frac{-17}{18}))b+\frac{255}{144} & \text{Neem samen} \\ &=b^2-\frac{203}{72}b+\frac{255}{144} & \text{Maak de som} \\ &=b^2-\frac{203}{72}b+\frac{85}{48} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-12 23:05:56
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