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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-19}{15})(17+b)& =(\color{red}{q}+\color{orange}{\frac{19}{15}}).(\color{green}{b}+\color{blue}{17})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(17)} + \color{orange}{(\frac{19}{15})} . \color{green}{(b)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = bq+17q+\frac{19}{15}b+\frac{19}{15}.17& \text{Uitwerken } \\ & =bq+17q+\frac{19}{15}b+\frac{323}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{4}-q)(\frac{3}{18}-b)& =(\color{red}{-q}+\color{orange}{2}).(\color{green}{-b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(2)} . \color{green}{(-b)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{6}q-2b+2.\frac{1}{6}& \text{Uitwerken } \\ & =bq-\frac{1}{6}q-2b+\frac{2}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{6}q-2b+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-1}{10})(\frac{-15}{16}-b)& =(\color{red}{q}+\color{orange}{\frac{-1}{10}}).(\color{green}{-b}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{15}{16}q+\frac{1}{10}b+\frac{1}{10}.\frac{15}{16}& \text{Uitwerken } \\ & =-bq-\frac{15}{16}q+\frac{1}{10}b+\frac{15}{160} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{15}{16}q+\frac{1}{10}b+\frac{3}{32} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-4}{8}-x)(\frac{-16}{13}+b)& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{16}{13}x-\frac{1}{2}b+\frac{1}{2}.\frac{16}{13}& \text{Uitwerken } \\ & =-bx+\frac{16}{13}x-\frac{1}{2}b+\frac{16}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{16}{13}x-\frac{1}{2}b+\frac{8}{13} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b-\frac{10}{17})(q+\frac{1}{4})& =(\color{red}{b}+\color{orange}{\frac{-10}{17}}).(\color{green}{q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-10}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{4}b-\frac{10}{17}q-\frac{10}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =bq+\frac{1}{4}b-\frac{10}{17}q-\frac{10}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{1}{4}b-\frac{10}{17}q-\frac{5}{34} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-11}{11})(\frac{-5}{6}-p)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{5}{6}p-1p-1.\frac{5}{6}& \text{Uitwerken } \\ & =-p^2+((\frac{-5}{6})+(-1))p-\frac{5}{6} & \text{Neem samen} \\ &=-p^2-\frac{11}{6}p-\frac{5}{6} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(x+\frac{-9}{12})(a+\frac{-12}{7})& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{-12}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{7})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-12}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{12}{7}x-\frac{3}{4}a+\frac{3}{4}.\frac{12}{7}& \text{Uitwerken } \\ & =ax-\frac{12}{7}x-\frac{3}{4}a+\frac{36}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{12}{7}x-\frac{3}{4}a+\frac{9}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-20}{14}-p)(\frac{7}{16}-p)& =(\color{red}{-p}+\color{orange}{\frac{-10}{7}}).(\color{green}{-p}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{7}{16}p+\frac{10}{7}p-\frac{10}{7}.\frac{7}{16}& \text{Uitwerken } \\ & =p^2+((\frac{-7}{16})+\frac{10}{7})p-(\frac{-70}{112}) & \text{Neem samen} \\ &=p^2+\frac{111}{112}p-(\frac{-70}{112}) & \text{Maak de som} \\ &=p^2+\frac{111}{112}p+\frac{5}{8} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{-16}{18}-b)(q-\frac{5}{20})& =(\color{red}{-b}+\color{orange}{\frac{-8}{9}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{4}b-\frac{8}{9}q+\frac{8}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =-bq+\frac{1}{4}b-\frac{8}{9}q+\frac{8}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{1}{4}b-\frac{8}{9}q+\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-19}{10})(\frac{-12}{5}+p)& =(\color{red}{a}+\color{orange}{\frac{19}{10}}).(\color{green}{p}+\color{blue}{\frac{-12}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{5})} + \color{orange}{(\frac{19}{10})} . \color{green}{(p)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{-12}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{12}{5}a+\frac{19}{10}p-\frac{19}{10}.\frac{12}{5}& \text{Uitwerken } \\ & =ap-\frac{12}{5}a+\frac{19}{10}p-\frac{228}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{12}{5}a+\frac{19}{10}p-\frac{114}{25} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-19}{2})(a-\frac{1}{18})& =(\color{red}{a}+\color{orange}{\frac{19}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{19}{2})} . \color{green}{(a)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{18}a+\frac{19}{2}a-\frac{19}{2}.\frac{1}{18}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{18})+\frac{19}{2})a-(\frac{-19}{36}) & \text{Neem samen} \\ &=a^2+\frac{170}{18}a-(\frac{-19}{36}) & \text{Maak de som} \\ &=a^2+\frac{85}{9}a+\frac{19}{36} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{7}{5}-b)(\frac{-7}{6}-q)& =(\color{red}{-b}+\color{orange}{\frac{7}{5}}).(\color{green}{-q}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{7}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{6}b-\frac{7}{5}q-\frac{7}{5}.\frac{7}{6}& \text{Uitwerken } \\ & =bq+\frac{7}{6}b-\frac{7}{5}q-\frac{49}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-03 05:19:30