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

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

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Verbetersleutel

  1. \(\begin{align}(x+\frac{12}{13})(\frac{-2}{14}-b)& =(\color{red}{x}+\color{orange}{\frac{12}{13}}).(\color{green}{-b}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{12}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{12}{13})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{7}x-\frac{12}{13}b-\frac{12}{13}.\frac{1}{7}& \text{Uitwerken } \\ & =-bx-\frac{1}{7}x-\frac{12}{13}b-\frac{12}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-11}{6}-a)(\frac{11}{13}-x)& =(\color{red}{-a}+\color{orange}{\frac{-11}{6}}).(\color{green}{-x}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{13}a+\frac{11}{6}x-\frac{11}{6}.\frac{11}{13}& \text{Uitwerken } \\ & =ax-\frac{11}{13}a+\frac{11}{6}x-\frac{121}{78} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-8}{17}+q)(q-\frac{10}{13})& =(\color{red}{q}+\color{orange}{\frac{-8}{17}}).(\color{green}{q}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{10}{13}q-\frac{8}{17}q+\frac{8}{17}.\frac{10}{13}& \text{Uitwerken } \\ & =q^2+((\frac{-10}{13})+(\frac{-8}{17}))q+\frac{80}{221} & \text{Neem samen} \\ &=q^2-\frac{274}{221}q+\frac{80}{221} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{14}{17}-b)(b-\frac{-7}{3})& =(\color{red}{-b}+\color{orange}{\frac{14}{17}}).(\color{green}{b}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{14}{17})} . \color{green}{(b)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{7}{3}b+\frac{14}{17}b+\frac{14}{17}.\frac{7}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-7}{3})+\frac{14}{17})b+(\frac{-98}{51}) & \text{Neem samen} \\ &=-b^2-\frac{77}{51}b+(\frac{-98}{51}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(x-\frac{-13}{5})(b-13)& =(\color{red}{x}+\color{orange}{\frac{13}{5}}).(\color{green}{b}+\color{blue}{(-13)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-13)} + \color{orange}{(\frac{13}{5})} . \color{green}{(b)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = bx-13x+\frac{13}{5}b-\frac{13}{5}.13& \text{Uitwerken } \\ & =bx-13x+\frac{13}{5}b-\frac{169}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{16}{5})(\frac{7}{14}+x)& =(\color{red}{a}+\color{orange}{\frac{-16}{5}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}a-\frac{16}{5}x-\frac{16}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}a-\frac{16}{5}x-\frac{16}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{2}a-\frac{16}{5}x-\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{16}{12}-x)(\frac{-12}{17}+q)& =(\color{red}{-x}+\color{orange}{\frac{4}{3}}).(\color{green}{q}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{12}{17}x+\frac{4}{3}q-\frac{4}{3}.\frac{12}{17}& \text{Uitwerken } \\ & =-qx+\frac{12}{17}x+\frac{4}{3}q-\frac{48}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{12}{17}x+\frac{4}{3}q-\frac{16}{17} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-13}{10})(\frac{-19}{5}-a)& =(\color{red}{a}+\color{orange}{\frac{13}{10}}).(\color{green}{-a}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{13}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{19}{5}a-\frac{13}{10}a-\frac{13}{10}.\frac{19}{5}& \text{Uitwerken } \\ & =-a^2+((\frac{-19}{5})+(\frac{-13}{10}))a-\frac{247}{50} & \text{Neem samen} \\ &=-a^2-\frac{51}{10}a-\frac{247}{50} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{8}{4}+a)(\frac{4}{3}-b)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{-b}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(2)} . \color{green}{(-b)} + \color{orange}{(2)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{4}{3}a-2b+2.\frac{4}{3}& \text{Uitwerken } \\ & =-ab+\frac{4}{3}a-2b+\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-8}{16}+a)(\frac{5}{7}-q)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{-q}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{7}a+\frac{1}{2}q-\frac{1}{2}.\frac{5}{7}& \text{Uitwerken } \\ & =-aq+\frac{5}{7}a+\frac{1}{2}q-\frac{5}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{20}{9})(a+\frac{-12}{2})& =(\color{red}{b}+\color{orange}{\frac{-20}{9}}).(\color{green}{a}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-6)} + \color{orange}{(\frac{-20}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ab-6b-\frac{20}{9}a+\frac{20}{9}.6& \text{Uitwerken } \\ & =ab-6b-\frac{20}{9}a+\frac{120}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-6b-\frac{20}{9}a+\frac{40}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{15}-a)(p-\frac{14}{14})& =(\color{red}{-a}+\color{orange}{\frac{-6}{5}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-6}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1a-\frac{6}{5}p+\frac{6}{5}.1& \text{Uitwerken } \\ & =-ap+1a-\frac{6}{5}p+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-02 15:22:11
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