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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+20)(q-\frac{-20}{10})& =(\color{red}{a}+\color{orange}{20}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(20)} . \color{green}{(q)} + \color{orange}{(20)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq+2a+20q+20.2& \text{Uitwerken } \\ & =aq+2a+20q+40 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{-9}{5})(\frac{3}{10}+p)& =(\color{red}{x}+\color{orange}{\frac{-9}{5}}).(\color{green}{p}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{10}x-\frac{9}{5}p-\frac{9}{5}.\frac{3}{10}& \text{Uitwerken } \\ & =px+\frac{3}{10}x-\frac{9}{5}p-\frac{27}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{5}{19})(q+\frac{-11}{13})& =(\color{red}{p}+\color{orange}{\frac{-5}{19}}).(\color{green}{q}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{13}p-\frac{5}{19}q+\frac{5}{19}.\frac{11}{13}& \text{Uitwerken } \\ & =pq-\frac{11}{13}p-\frac{5}{19}q+\frac{55}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-8}{4})(\frac{-2}{17}+q)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{2}{17}q+2q-2.\frac{2}{17}& \text{Uitwerken } \\ & =q^2+((\frac{-2}{17})+2)q-(\frac{-4}{17}) & \text{Neem samen} \\ &=q^2+\frac{32}{17}q-(\frac{-4}{17}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-14}{9}+a)(\frac{10}{4}-b)& =(\color{red}{a}+\color{orange}{\frac{-14}{9}}).(\color{green}{-b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{2}a+\frac{14}{9}b-\frac{14}{9}.\frac{5}{2}& \text{Uitwerken } \\ & =-ab+\frac{5}{2}a+\frac{14}{9}b-\frac{70}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{2}a+\frac{14}{9}b-\frac{35}{9} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-\frac{1}{19})(p-\frac{17}{13})& =(\color{red}{a}+\color{orange}{\frac{-1}{19}}).(\color{green}{p}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{-1}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{17}{13}a-\frac{1}{19}p+\frac{1}{19}.\frac{17}{13}& \text{Uitwerken } \\ & =ap-\frac{17}{13}a-\frac{1}{19}p+\frac{17}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-9}{5})(\frac{-9}{6}+q)& =(\color{red}{b}+\color{orange}{\frac{9}{5}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{9}{5})} . \color{green}{(q)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{2}b+\frac{9}{5}q-\frac{9}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =bq-\frac{3}{2}b+\frac{9}{5}q-\frac{27}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{8}{16})((-3)-q)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{-q}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bq-3b-\frac{1}{2}q-\frac{1}{2}.3& \text{Uitwerken } \\ & =-bq-3b-\frac{1}{2}q-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{7}{2})(\frac{-4}{2}+a)& =(\color{red}{p}+\color{orange}{\frac{-7}{2}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ap-2p-\frac{7}{2}a+\frac{7}{2}.2& \text{Uitwerken } \\ & =ap-2p-\frac{7}{2}a+\frac{14}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-2p-\frac{7}{2}a+7 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q+15)(\frac{-18}{14}-a)& =(\color{red}{q}+\color{orange}{15}).(\color{green}{-a}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(15)} . \color{green}{(-a)} + \color{orange}{(15)} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{9}{7}q-15a-15.\frac{9}{7}& \text{Uitwerken } \\ & =-aq-\frac{9}{7}q-15a-\frac{135}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-4}{7})(a+\frac{-19}{19})& =(\color{red}{p}+\color{orange}{\frac{-4}{7}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1p-\frac{4}{7}a+\frac{4}{7}.1& \text{Uitwerken } \\ & =ap-1p-\frac{4}{7}a+\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-19}{5})(\frac{5}{10}+a)& =(\color{red}{b}+\color{orange}{\frac{-19}{5}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}b-\frac{19}{5}a-\frac{19}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}b-\frac{19}{5}a-\frac{19}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-07 06:41:35
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