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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{19}{6})(a-\frac{-12}{15})& =(\color{red}{q}+\color{orange}{\frac{-19}{6}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{5}q-\frac{19}{6}a-\frac{19}{6}.\frac{4}{5}& \text{Uitwerken } \\ & =aq+\frac{4}{5}q-\frac{19}{6}a-\frac{76}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{4}{5}q-\frac{19}{6}a-\frac{38}{15} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{1}{6})(a-\frac{-2}{9})& =(\color{red}{a}+\color{orange}{\frac{-1}{6}}).(\color{green}{a}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{2}{9}a-\frac{1}{6}a-\frac{1}{6}.\frac{2}{9}& \text{Uitwerken } \\ & =a^2+(\frac{2}{9}+(\frac{-1}{6}))a-(\frac{-2}{54}) & \text{Neem samen} \\ &=a^2+\frac{1}{18}a-(\frac{-2}{54}) & \text{Maak de som} \\ &=a^2+\frac{1}{18}a+\frac{1}{27} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{-2}{7}+a)(\frac{-4}{12}+x)& =(\color{red}{a}+\color{orange}{\frac{-2}{7}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{3}a-\frac{2}{7}x+\frac{2}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =ax-\frac{1}{3}a-\frac{2}{7}x+\frac{2}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{12}{10}+x)(q-\frac{10}{3})& =(\color{red}{x}+\color{orange}{\frac{6}{5}}).(\color{green}{q}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{6}{5})} . \color{green}{(q)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{10}{3}x+\frac{6}{5}q-\frac{6}{5}.\frac{10}{3}& \text{Uitwerken } \\ & =qx-\frac{10}{3}x+\frac{6}{5}q-\frac{60}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{10}{3}x+\frac{6}{5}q-4 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-18}{7}+p)(\frac{-13}{17}+a)& =(\color{red}{p}+\color{orange}{\frac{-18}{7}}).(\color{green}{a}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{17}p-\frac{18}{7}a+\frac{18}{7}.\frac{13}{17}& \text{Uitwerken } \\ & =ap-\frac{13}{17}p-\frac{18}{7}a+\frac{234}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-19}{3}-q)(\frac{12}{10}-p)& =(\color{red}{-q}+\color{orange}{\frac{-19}{3}}).(\color{green}{-p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{6}{5}q+\frac{19}{3}p-\frac{19}{3}.\frac{6}{5}& \text{Uitwerken } \\ & =pq-\frac{6}{5}q+\frac{19}{3}p-\frac{114}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{6}{5}q+\frac{19}{3}p-\frac{38}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a+\frac{-19}{19})(x+\frac{-13}{7})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{7}a-1x+1.\frac{13}{7}& \text{Uitwerken } \\ & =ax-\frac{13}{7}a-1x+\frac{13}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{10}{13}+p)(p-\frac{-13}{10})& =(\color{red}{p}+\color{orange}{\frac{10}{13}}).(\color{green}{p}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{10}{13})} . \color{green}{(p)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{13}{10}p+\frac{10}{13}p+\frac{10}{13}.\frac{13}{10}& \text{Uitwerken } \\ & =p^2+(\frac{13}{10}+\frac{10}{13})p+\frac{130}{130} & \text{Neem samen} \\ &=p^2+\frac{269}{130}p+\frac{130}{130} & \text{Maak de som} \\ &=p^2+\frac{269}{130}p+1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(6-b)(\frac{20}{18}-b)& =(\color{red}{-b}+\color{orange}{6}).(\color{green}{-b}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(6)} . \color{green}{(-b)} + \color{orange}{(6)} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{10}{9}b-6b+6.\frac{10}{9}& \text{Uitwerken } \\ & =b^2+((\frac{-10}{9})+(-6))b+\frac{60}{9} & \text{Neem samen} \\ &=b^2-\frac{64}{9}b+\frac{60}{9} & \text{Maak de som} \\ &=b^2-\frac{64}{9}b+\frac{20}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-19}{15})(b-\frac{-4}{18})& =(\color{red}{a}+\color{orange}{\frac{19}{15}}).(\color{green}{b}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{19}{15})} . \color{green}{(b)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{9}a+\frac{19}{15}b+\frac{19}{15}.\frac{2}{9}& \text{Uitwerken } \\ & =ab+\frac{2}{9}a+\frac{19}{15}b+\frac{38}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{3}+a)(q+\frac{8}{5})& =(\color{red}{a}+\color{orange}{\frac{16}{3}}).(\color{green}{q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{16}{3})} . \color{green}{(q)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{5}a+\frac{16}{3}q+\frac{16}{3}.\frac{8}{5}& \text{Uitwerken } \\ & =aq+\frac{8}{5}a+\frac{16}{3}q+\frac{128}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-20}{14}-b)(\frac{-18}{3}+q)& =(\color{red}{-b}+\color{orange}{\frac{-10}{7}}).(\color{green}{q}+\color{blue}{(-6)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(-6)} + \color{orange}{(\frac{-10}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -bq+6b-\frac{10}{7}q+\frac{10}{7}.6& \text{Uitwerken } \\ & =-bq+6b-\frac{10}{7}q+\frac{60}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-12 00:08:02
Een site van Busleyden Atheneum Mechelen