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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{11}+p)(\frac{-5}{9}-b)& =(\color{red}{p}+\color{orange}{\frac{9}{11}}).(\color{green}{-b}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{9}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{5}{9}p-\frac{9}{11}b-\frac{9}{11}.\frac{5}{9}& \text{Uitwerken } \\ & =-bp-\frac{5}{9}p-\frac{9}{11}b-\frac{45}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{5}{9}p-\frac{9}{11}b-\frac{5}{11} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{18}+b)(\frac{5}{5}+a)& =(\color{red}{b}+\color{orange}{\frac{4}{9}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1b+\frac{4}{9}a+\frac{4}{9}.1& \text{Uitwerken } \\ & =ab+1b+\frac{4}{9}a+\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{19}{6})(\frac{-7}{3}-b)& =(\color{red}{a}+\color{orange}{\frac{19}{6}}).(\color{green}{-b}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{19}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{6})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{7}{3}a-\frac{19}{6}b-\frac{19}{6}.\frac{7}{3}& \text{Uitwerken } \\ & =-ab-\frac{7}{3}a-\frac{19}{6}b-\frac{133}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-8}{6})(\frac{-4}{5}+b)& =(\color{red}{x}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{4}{5}x+\frac{4}{3}b-\frac{4}{3}.\frac{4}{5}& \text{Uitwerken } \\ & =bx-\frac{4}{5}x+\frac{4}{3}b-\frac{16}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{15}{5}-b)(b-\frac{-3}{11})& =(\color{red}{-b}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{11})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{3}{11}b+3b+3.\frac{3}{11}& \text{Uitwerken } \\ & =-b^2+((\frac{-3}{11})+3)b+(\frac{-9}{11}) & \text{Neem samen} \\ &=-b^2+\frac{30}{11}b+(\frac{-9}{11}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-4}{16})(\frac{15}{20}-p)& =(\color{red}{p}+\color{orange}{\frac{-1}{4}}).(\color{green}{-p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{3}{4}p+\frac{1}{4}p-\frac{1}{4}.\frac{3}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{3}{4}+\frac{1}{4})p-\frac{3}{16} & \text{Neem samen} \\ &=-p^2+\frac{4}{4}p-\frac{3}{16} & \text{Maak de som} \\ &=-p^2+1p-\frac{3}{16} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{18}{11}+b)(\frac{13}{18}-b)& =(\color{red}{b}+\color{orange}{\frac{18}{11}}).(\color{green}{-b}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{18}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{13}{18}b-\frac{18}{11}b+\frac{18}{11}.\frac{13}{18}& \text{Uitwerken } \\ & =-b^2+(\frac{13}{18}+(\frac{-18}{11}))b+(\frac{-234}{198}) & \text{Neem samen} \\ &=-b^2-\frac{181}{198}b+(\frac{-234}{198}) & \text{Maak de som} \\ &=-b^2-\frac{181}{198}b+(\frac{-13}{11}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(x+\frac{19}{9})(\frac{10}{11}+a)& =(\color{red}{x}+\color{orange}{\frac{19}{9}}).(\color{green}{a}+\color{blue}{\frac{10}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{10}{11})} + \color{orange}{(\frac{19}{9})} . \color{green}{(a)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{10}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{10}{11}x+\frac{19}{9}a+\frac{19}{9}.\frac{10}{11}& \text{Uitwerken } \\ & =ax+\frac{10}{11}x+\frac{19}{9}a+\frac{190}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{9}{9})(\frac{9}{19}+p)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{19}p-1p-1.\frac{9}{19}& \text{Uitwerken } \\ & =p^2+(\frac{9}{19}+(-1))p-(\frac{-9}{19}) & \text{Neem samen} \\ &=p^2-\frac{10}{19}p-(\frac{-9}{19}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(q-\frac{10}{16})(\frac{-2}{6}+x)& =(\color{red}{q}+\color{orange}{\frac{-5}{8}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{3}q-\frac{5}{8}x+\frac{5}{8}.\frac{1}{3}& \text{Uitwerken } \\ & =qx-\frac{1}{3}q-\frac{5}{8}x+\frac{5}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-9}{17}-q)(q-\frac{-19}{3})& =(\color{red}{-q}+\color{orange}{\frac{-9}{17}}).(\color{green}{q}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{19}{3}q-\frac{9}{17}q-\frac{9}{17}.\frac{19}{3}& \text{Uitwerken } \\ & =-q^2+((\frac{-19}{3})+(\frac{-9}{17}))q-\frac{171}{51} & \text{Neem samen} \\ &=-q^2-\frac{350}{51}q-\frac{171}{51} & \text{Maak de som} \\ &=-q^2-\frac{350}{51}q-\frac{57}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-12}{11})(\frac{10}{7}-q)& =(\color{red}{b}+\color{orange}{\frac{12}{11}}).(\color{green}{-q}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{12}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{10}{7}b-\frac{12}{11}q+\frac{12}{11}.\frac{10}{7}& \text{Uitwerken } \\ & =-bq+\frac{10}{7}b-\frac{12}{11}q+\frac{120}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-26 14:58:16
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