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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-5}{10}-q)(\frac{-13}{17}-q)& =(\color{red}{-q}+\color{orange}{\frac{-1}{2}}).(\color{green}{-q}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{13}{17}q+\frac{1}{2}q+\frac{1}{2}.\frac{13}{17}& \text{Uitwerken } \\ & =q^2+(\frac{13}{17}+\frac{1}{2})q+\frac{13}{34} & \text{Neem samen} \\ &=q^2+\frac{43}{34}q+\frac{13}{34} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(p+(-3))(\frac{6}{12}-a)& =(\color{red}{p}+\color{orange}{(-3)}).(\color{green}{-a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-3)} . \color{green}{(-a)} + \color{orange}{(-3)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{2}p+3a-3.\frac{1}{2}& \text{Uitwerken } \\ & =-ap+\frac{1}{2}p+3a-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{14}{5}+b)(\frac{11}{12}+x)& =(\color{red}{b}+\color{orange}{\frac{14}{5}}).(\color{green}{x}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{14}{5})} . \color{green}{(x)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{12}b+\frac{14}{5}x+\frac{14}{5}.\frac{11}{12}& \text{Uitwerken } \\ & =bx+\frac{11}{12}b+\frac{14}{5}x+\frac{154}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{11}{12}b+\frac{14}{5}x+\frac{77}{30} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-14}{7}+a)(a+\frac{-17}{20})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{17}{20}a-2a+2.\frac{17}{20}& \text{Uitwerken } \\ & =a^2+((\frac{-17}{20})+(-2))a+\frac{34}{20} & \text{Neem samen} \\ &=a^2-\frac{57}{20}a+\frac{34}{20} & \text{Maak de som} \\ &=a^2-\frac{57}{20}a+\frac{17}{10} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-17}{3})(\frac{19}{3}-x)& =(\color{red}{x}+\color{orange}{\frac{-17}{3}}).(\color{green}{-x}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{19}{3}x+\frac{17}{3}x-\frac{17}{3}.\frac{19}{3}& \text{Uitwerken } \\ & =-x^2+(\frac{19}{3}+\frac{17}{3})x-\frac{323}{9} & \text{Neem samen} \\ &=-x^2+\frac{36}{3}x-\frac{323}{9} & \text{Maak de som} \\ &=-x^2+12x-\frac{323}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{5}{20}-p)(\frac{-8}{19}-a)& =(\color{red}{-p}+\color{orange}{\frac{1}{4}}).(\color{green}{-a}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{19}p-\frac{1}{4}a-\frac{1}{4}.\frac{8}{19}& \text{Uitwerken } \\ & =ap+\frac{8}{19}p-\frac{1}{4}a-\frac{8}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{8}{19}p-\frac{1}{4}a-\frac{2}{19} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x+\frac{-14}{18})(\frac{-1}{20}-a)& =(\color{red}{x}+\color{orange}{\frac{-7}{9}}).(\color{green}{-a}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{20}x+\frac{7}{9}a+\frac{7}{9}.\frac{1}{20}& \text{Uitwerken } \\ & =-ax-\frac{1}{20}x+\frac{7}{9}a+\frac{7}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{20}{16})(q+13)& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{q}+\color{blue}{13})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(13)} + \color{orange}{(\frac{-5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = qx+13x-\frac{5}{4}q-\frac{5}{4}.13& \text{Uitwerken } \\ & =qx+13x-\frac{5}{4}q-\frac{65}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-2}{9}-p)(\frac{-4}{9}-q)& =(\color{red}{-p}+\color{orange}{\frac{-2}{9}}).(\color{green}{-q}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{9}p+\frac{2}{9}q+\frac{2}{9}.\frac{4}{9}& \text{Uitwerken } \\ & =pq+\frac{4}{9}p+\frac{2}{9}q+\frac{8}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{11}{13})(q-\frac{19}{12})& =(\color{red}{p}+\color{orange}{\frac{-11}{13}}).(\color{green}{q}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{12}p-\frac{11}{13}q+\frac{11}{13}.\frac{19}{12}& \text{Uitwerken } \\ & =pq-\frac{19}{12}p-\frac{11}{13}q+\frac{209}{156} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{1}{20})(b+(-8))& =(\color{red}{q}+\color{orange}{\frac{1}{20}}).(\color{green}{b}+\color{blue}{(-8)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-8)} + \color{orange}{(\frac{1}{20})} . \color{green}{(b)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = bq-8q+\frac{1}{20}b-\frac{1}{20}.8& \text{Uitwerken } \\ & =bq-8q+\frac{1}{20}b-\frac{8}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-8q+\frac{1}{20}b-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{19}{16}-b)(\frac{-13}{10}+p)& =(\color{red}{-b}+\color{orange}{\frac{19}{16}}).(\color{green}{p}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{19}{16})} . \color{green}{(p)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{10}b+\frac{19}{16}p-\frac{19}{16}.\frac{13}{10}& \text{Uitwerken } \\ & =-bp+\frac{13}{10}b+\frac{19}{16}p-\frac{247}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-16 18:03:51
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