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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{18}{16})(b+\frac{-18}{20})& =(\color{red}{a}+\color{orange}{\frac{9}{8}}).(\color{green}{b}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{10}a+\frac{9}{8}b-\frac{9}{8}.\frac{9}{10}& \text{Uitwerken } \\ & =ab-\frac{9}{10}a+\frac{9}{8}b-\frac{81}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(5-q)(b+\frac{-16}{14})& =(\color{red}{-q}+\color{orange}{5}).(\color{green}{b}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(5)} . \color{green}{(b)} + \color{orange}{(5)} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{8}{7}q+5b-5.\frac{8}{7}& \text{Uitwerken } \\ & =-bq+\frac{8}{7}q+5b-\frac{40}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-8}{2}+a)(\frac{20}{7}-b)& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{-b}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(-4)} . \color{green}{(-b)} + \color{orange}{(-4)} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{20}{7}a+4b-4.\frac{20}{7}& \text{Uitwerken } \\ & =-ab+\frac{20}{7}a+4b-\frac{80}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-15}{5})(x+\frac{-14}{20})& =(\color{red}{a}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{10}a+3x-3.\frac{7}{10}& \text{Uitwerken } \\ & =ax-\frac{7}{10}a+3x-\frac{21}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-3}{8})(x+\frac{19}{12})& =(\color{red}{p}+\color{orange}{\frac{3}{8}}).(\color{green}{x}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{3}{8})} . \color{green}{(x)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{19}{12}p+\frac{3}{8}x+\frac{3}{8}.\frac{19}{12}& \text{Uitwerken } \\ & =px+\frac{19}{12}p+\frac{3}{8}x+\frac{57}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{19}{12}p+\frac{3}{8}x+\frac{19}{32} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{6}{14})(x-\frac{13}{9})& =(\color{red}{q}+\color{orange}{\frac{-3}{7}}).(\color{green}{x}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{9}q-\frac{3}{7}x+\frac{3}{7}.\frac{13}{9}& \text{Uitwerken } \\ & =qx-\frac{13}{9}q-\frac{3}{7}x+\frac{39}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{13}{9}q-\frac{3}{7}x+\frac{13}{21} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x+\frac{4}{3})(b+\frac{15}{4})& =(\color{red}{x}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{4}x+\frac{4}{3}b+\frac{4}{3}.\frac{15}{4}& \text{Uitwerken } \\ & =bx+\frac{15}{4}x+\frac{4}{3}b+\frac{60}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{15}{4}x+\frac{4}{3}b+5 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{4}{3})(p-\frac{18}{4})& =(\color{red}{x}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{2}x-\frac{4}{3}p+\frac{4}{3}.\frac{9}{2}& \text{Uitwerken } \\ & =px-\frac{9}{2}x-\frac{4}{3}p+\frac{36}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{9}{2}x-\frac{4}{3}p+6 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-19}{4})(a+\frac{5}{8})& =(\color{red}{q}+\color{orange}{\frac{19}{4}}).(\color{green}{a}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{19}{4})} . \color{green}{(a)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{8}q+\frac{19}{4}a+\frac{19}{4}.\frac{5}{8}& \text{Uitwerken } \\ & =aq+\frac{5}{8}q+\frac{19}{4}a+\frac{95}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{6}{11}-q)(19-q)& =(\color{red}{-q}+\color{orange}{\frac{6}{11}}).(\color{green}{-q}+\color{blue}{19})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(19)} + \color{orange}{(\frac{6}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = qq-19q-\frac{6}{11}q+\frac{6}{11}.19& \text{Uitwerken } \\ & =q^2+((-19)+(\frac{-6}{11}))q+\frac{114}{11} & \text{Neem samen} \\ &=q^2-\frac{215}{11}q+\frac{114}{11} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-20}{12})(\frac{-19}{8}-x)& =(\color{red}{a}+\color{orange}{\frac{5}{3}}).(\color{green}{-x}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{19}{8}a-\frac{5}{3}x-\frac{5}{3}.\frac{19}{8}& \text{Uitwerken } \\ & =-ax-\frac{19}{8}a-\frac{5}{3}x-\frac{95}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-11}{3})(\frac{-2}{8}-b)& =(\color{red}{q}+\color{orange}{\frac{-11}{3}}).(\color{green}{-b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{4}q+\frac{11}{3}b+\frac{11}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =-bq-\frac{1}{4}q+\frac{11}{3}b+\frac{11}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-18 11:29:02
Een site van Busleyden Atheneum Mechelen