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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-1}{13})(a-\frac{8}{9})& =(\color{red}{a}+\color{orange}{\frac{1}{13}}).(\color{green}{a}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{1}{13})} . \color{green}{(a)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{8}{9}a+\frac{1}{13}a-\frac{1}{13}.\frac{8}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-8}{9})+\frac{1}{13})a-(\frac{-8}{117}) & \text{Neem samen} \\ &=a^2-\frac{95}{117}a-(\frac{-8}{117}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{2}+a)(\frac{20}{18}+q)& =(\color{red}{a}+\color{orange}{\frac{19}{2}}).(\color{green}{q}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{19}{2})} . \color{green}{(q)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{9}a+\frac{19}{2}q+\frac{19}{2}.\frac{10}{9}& \text{Uitwerken } \\ & =aq+\frac{10}{9}a+\frac{19}{2}q+\frac{190}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{10}{9}a+\frac{19}{2}q+\frac{95}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-9}{7}-a)(a-\frac{12}{19})& =(\color{red}{-a}+\color{orange}{\frac{-9}{7}}).(\color{green}{a}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{12}{19}a-\frac{9}{7}a+\frac{9}{7}.\frac{12}{19}& \text{Uitwerken } \\ & =-a^2+(\frac{12}{19}+(\frac{-9}{7}))a+(\frac{-108}{133}) & \text{Neem samen} \\ &=-a^2-\frac{87}{133}a+(\frac{-108}{133}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-20}{2}-a)(\frac{-4}{8}+a)& =(\color{red}{-a}+\color{orange}{(-10)}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-10)} . \color{green}{(a)} + \color{orange}{(-10)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{2}a-10a+10.\frac{1}{2}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{2}+(-10))a+(\frac{-10}{2}) & \text{Neem samen} \\ &=-a^2-\frac{19}{2}a+(\frac{-10}{2}) & \text{Maak de som} \\ &=-a^2-\frac{19}{2}a+(-5) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-11}{15})(b-\frac{-10}{13})& =(\color{red}{q}+\color{orange}{\frac{-11}{15}}).(\color{green}{b}+\color{blue}{\frac{10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{10}{13})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{10}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{10}{13}q-\frac{11}{15}b-\frac{11}{15}.\frac{10}{13}& \text{Uitwerken } \\ & =bq+\frac{10}{13}q-\frac{11}{15}b-\frac{110}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{10}{13}q-\frac{11}{15}b-\frac{22}{39} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p+\frac{1}{18})(\frac{-7}{6}+x)& =(\color{red}{p}+\color{orange}{\frac{1}{18}}).(\color{green}{x}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{1}{18})} . \color{green}{(x)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{6}p+\frac{1}{18}x-\frac{1}{18}.\frac{7}{6}& \text{Uitwerken } \\ & =px-\frac{7}{6}p+\frac{1}{18}x-\frac{7}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{17}{3})(b+\frac{10}{18})& =(\color{red}{q}+\color{orange}{\frac{17}{3}}).(\color{green}{b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{17}{3})} . \color{green}{(b)} + \color{orange}{(\frac{17}{3})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{9}q+\frac{17}{3}b+\frac{17}{3}.\frac{5}{9}& \text{Uitwerken } \\ & =bq+\frac{5}{9}q+\frac{17}{3}b+\frac{85}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{17}{16})(\frac{-4}{6}+q)& =(\color{red}{a}+\color{orange}{\frac{-17}{16}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{3}a-\frac{17}{16}q+\frac{17}{16}.\frac{2}{3}& \text{Uitwerken } \\ & =aq-\frac{2}{3}a-\frac{17}{16}q+\frac{34}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{2}{3}a-\frac{17}{16}q+\frac{17}{24} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-4}{10})(q-\frac{-19}{19})& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1p-\frac{2}{5}q-\frac{2}{5}.1& \text{Uitwerken } \\ & =pq+1p-\frac{2}{5}q-\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-7}{2})(\frac{-15}{5}-b)& =(\color{red}{p}+\color{orange}{\frac{-7}{2}}).(\color{green}{-b}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{-7}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bp-3p+\frac{7}{2}b+\frac{7}{2}.3& \text{Uitwerken } \\ & =-bp-3p+\frac{7}{2}b+\frac{21}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-18}{3}+b)(q-\frac{13}{3})& =(\color{red}{b}+\color{orange}{(-6)}).(\color{green}{q}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(-6)} . \color{green}{(q)} + \color{orange}{(-6)} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{3}b-6q+6.\frac{13}{3}& \text{Uitwerken } \\ & =bq-\frac{13}{3}b-6q+\frac{78}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{13}{3}b-6q+26 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-1}{20})(\frac{-15}{18}-q)& =(\color{red}{b}+\color{orange}{\frac{-1}{20}}).(\color{green}{-q}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{-1}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{6}b+\frac{1}{20}q+\frac{1}{20}.\frac{5}{6}& \text{Uitwerken } \\ & =-bq-\frac{5}{6}b+\frac{1}{20}q+\frac{5}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{5}{6}b+\frac{1}{20}q+\frac{1}{24} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-28 15:14:51
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