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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-2}{14})(\frac{-5}{16}+x)& =(\color{red}{b}+\color{orange}{\frac{-1}{7}}).(\color{green}{x}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{16}b-\frac{1}{7}x+\frac{1}{7}.\frac{5}{16}& \text{Uitwerken } \\ & =bx-\frac{5}{16}b-\frac{1}{7}x+\frac{5}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-8}{7})(\frac{13}{4}-x)& =(\color{red}{b}+\color{orange}{\frac{8}{7}}).(\color{green}{-x}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{8}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{13}{4}b-\frac{8}{7}x+\frac{8}{7}.\frac{13}{4}& \text{Uitwerken } \\ & =-bx+\frac{13}{4}b-\frac{8}{7}x+\frac{104}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{13}{4}b-\frac{8}{7}x+\frac{26}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-1}{4})(p+\frac{-13}{16})& =(\color{red}{q}+\color{orange}{\frac{1}{4}}).(\color{green}{p}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{16}q+\frac{1}{4}p-\frac{1}{4}.\frac{13}{16}& \text{Uitwerken } \\ & =pq-\frac{13}{16}q+\frac{1}{4}p-\frac{13}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+5)(a+\frac{14}{10})& =(\color{red}{a}+\color{orange}{5}).(\color{green}{a}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(5)} . \color{green}{(a)} + \color{orange}{(5)} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{5}a+5a+5.\frac{7}{5}& \text{Uitwerken } \\ & =a^2+(\frac{7}{5}+5)a+\frac{35}{5} & \text{Neem samen} \\ &=a^2+\frac{32}{5}a+\frac{35}{5} & \text{Maak de som} \\ &=a^2+\frac{32}{5}a+7 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(q+\frac{20}{19})(x+\frac{-14}{17})& =(\color{red}{q}+\color{orange}{\frac{20}{19}}).(\color{green}{x}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{20}{19})} . \color{green}{(x)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{14}{17}q+\frac{20}{19}x-\frac{20}{19}.\frac{14}{17}& \text{Uitwerken } \\ & =qx-\frac{14}{17}q+\frac{20}{19}x-\frac{280}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-19}{4})(p-\frac{-6}{20})& =(\color{red}{a}+\color{orange}{\frac{19}{4}}).(\color{green}{p}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{19}{4})} . \color{green}{(p)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{10}a+\frac{19}{4}p+\frac{19}{4}.\frac{3}{10}& \text{Uitwerken } \\ & =ap+\frac{3}{10}a+\frac{19}{4}p+\frac{57}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-11}{17}-q)(b+\frac{20}{20})& =(\color{red}{-q}+\color{orange}{\frac{-11}{17}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{-11}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bq-1q-\frac{11}{17}b-\frac{11}{17}.1& \text{Uitwerken } \\ & =-bq-1q-\frac{11}{17}b-\frac{11}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{20}-p)(b-\frac{13}{13})& =(\color{red}{-p}+\color{orange}{\frac{9}{10}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(\frac{9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1p+\frac{9}{10}b-\frac{9}{10}.1& \text{Uitwerken } \\ & =-bp+1p+\frac{9}{10}b-\frac{9}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-20}{14}-x)(\frac{6}{19}+x)& =(\color{red}{-x}+\color{orange}{\frac{-10}{7}}).(\color{green}{x}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{6}{19}x-\frac{10}{7}x-\frac{10}{7}.\frac{6}{19}& \text{Uitwerken } \\ & =-x^2+((\frac{-6}{19})+(\frac{-10}{7}))x-\frac{60}{133} & \text{Neem samen} \\ &=-x^2-\frac{232}{133}x-\frac{60}{133} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-8}{17}+a)(b+\frac{4}{16})& =(\color{red}{a}+\color{orange}{\frac{-8}{17}}).(\color{green}{b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{4}a-\frac{8}{17}b-\frac{8}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =ab+\frac{1}{4}a-\frac{8}{17}b-\frac{8}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{4}a-\frac{8}{17}b-\frac{2}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{12}+x)(x+\frac{17}{18})& =(\color{red}{x}+\color{orange}{\frac{-13}{12}}).(\color{green}{x}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{17}{18}x-\frac{13}{12}x-\frac{13}{12}.\frac{17}{18}& \text{Uitwerken } \\ & =x^2+(\frac{17}{18}+(\frac{-13}{12}))x-(\frac{-221}{216}) & \text{Neem samen} \\ &=x^2-\frac{5}{36}x-(\frac{-221}{216}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-9}{5})(x-\frac{-7}{15})& =(\color{red}{a}+\color{orange}{\frac{-9}{5}}).(\color{green}{x}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{15}a-\frac{9}{5}x-\frac{9}{5}.\frac{7}{15}& \text{Uitwerken } \\ & =ax+\frac{7}{15}a-\frac{9}{5}x-\frac{63}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{7}{15}a-\frac{9}{5}x-\frac{21}{25} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-03 16:18:06
Een site van Busleyden Atheneum Mechelen