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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{16}{11}-a)(b+\frac{-9}{7})& =(\color{red}{-a}+\color{orange}{\frac{16}{11}}).(\color{green}{b}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{16}{11})} . \color{green}{(b)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{9}{7}a+\frac{16}{11}b-\frac{16}{11}.\frac{9}{7}& \text{Uitwerken } \\ & =-ab+\frac{9}{7}a+\frac{16}{11}b-\frac{144}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{11}-q)(b-\frac{19}{10})& =(\color{red}{-q}+\color{orange}{\frac{-12}{11}}).(\color{green}{b}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{19}{10}q-\frac{12}{11}b+\frac{12}{11}.\frac{19}{10}& \text{Uitwerken } \\ & =-bq+\frac{19}{10}q-\frac{12}{11}b+\frac{228}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{19}{10}q-\frac{12}{11}b+\frac{114}{55} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{4}{18}+a)(p-\frac{2}{13})& =(\color{red}{a}+\color{orange}{\frac{2}{9}}).(\color{green}{p}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{2}{9})} . \color{green}{(p)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{13}a+\frac{2}{9}p-\frac{2}{9}.\frac{2}{13}& \text{Uitwerken } \\ & =ap-\frac{2}{13}a+\frac{2}{9}p-\frac{4}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-17}{3})(\frac{-13}{16}-q)& =(\color{red}{a}+\color{orange}{\frac{-17}{3}}).(\color{green}{-q}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{13}{16}a+\frac{17}{3}q+\frac{17}{3}.\frac{13}{16}& \text{Uitwerken } \\ & =-aq-\frac{13}{16}a+\frac{17}{3}q+\frac{221}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{8}{20}+p)(a-\frac{-3}{18})& =(\color{red}{p}+\color{orange}{\frac{2}{5}}).(\color{green}{a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{6}p+\frac{2}{5}a+\frac{2}{5}.\frac{1}{6}& \text{Uitwerken } \\ & =ap+\frac{1}{6}p+\frac{2}{5}a+\frac{2}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{6}p+\frac{2}{5}a+\frac{1}{15} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-20}{6}+p)(\frac{1}{14}-a)& =(\color{red}{p}+\color{orange}{\frac{-10}{3}}).(\color{green}{-a}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{14}p+\frac{10}{3}a-\frac{10}{3}.\frac{1}{14}& \text{Uitwerken } \\ & =-ap+\frac{1}{14}p+\frac{10}{3}a-\frac{10}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{1}{14}p+\frac{10}{3}a-\frac{5}{21} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-16}{19})(\frac{-18}{8}-q)& =(\color{red}{a}+\color{orange}{\frac{16}{19}}).(\color{green}{-q}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{16}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{9}{4}a-\frac{16}{19}q-\frac{16}{19}.\frac{9}{4}& \text{Uitwerken } \\ & =-aq-\frac{9}{4}a-\frac{16}{19}q-\frac{144}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{9}{4}a-\frac{16}{19}q-\frac{36}{19} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{6}{14}+x)(x-\frac{-4}{9})& =(\color{red}{x}+\color{orange}{\frac{3}{7}}).(\color{green}{x}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{3}{7})} . \color{green}{(x)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{4}{9}x+\frac{3}{7}x+\frac{3}{7}.\frac{4}{9}& \text{Uitwerken } \\ & =x^2+(\frac{4}{9}+\frac{3}{7})x+\frac{12}{63} & \text{Neem samen} \\ &=x^2+\frac{55}{63}x+\frac{12}{63} & \text{Maak de som} \\ &=x^2+\frac{55}{63}x+\frac{4}{21} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{1}{10}-b)(\frac{17}{12}-b)& =(\color{red}{-b}+\color{orange}{\frac{1}{10}}).(\color{green}{-b}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{1}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{17}{12}b-\frac{1}{10}b+\frac{1}{10}.\frac{17}{12}& \text{Uitwerken } \\ & =b^2+((\frac{-17}{12})+(\frac{-1}{10}))b+\frac{17}{120} & \text{Neem samen} \\ &=b^2-\frac{91}{60}b+\frac{17}{120} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-16}{11})(x+\frac{18}{18})& =(\color{red}{b}+\color{orange}{\frac{16}{11}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{16}{11})} . \color{green}{(x)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1b+\frac{16}{11}x+\frac{16}{11}.1& \text{Uitwerken } \\ & =bx+1b+\frac{16}{11}x+\frac{16}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{2}+q)(q-\frac{-2}{14})& =(\color{red}{q}+\color{orange}{\frac{-13}{2}}).(\color{green}{q}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{7}q-\frac{13}{2}q-\frac{13}{2}.\frac{1}{7}& \text{Uitwerken } \\ & =q^2+(\frac{1}{7}+(\frac{-13}{2}))q-(\frac{-13}{14}) & \text{Neem samen} \\ &=q^2-\frac{89}{14}q-(\frac{-13}{14}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{2}-p)(a+\frac{-12}{7})& =(\color{red}{-p}+\color{orange}{4}).(\color{green}{a}+\color{blue}{\frac{-12}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-12}{7})} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(\frac{-12}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{12}{7}p+4a-4.\frac{12}{7}& \text{Uitwerken } \\ & =-ap+\frac{12}{7}p+4a-\frac{48}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-26 15:45:45
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