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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-4}{10})(\frac{11}{16}+q)& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{16}p-\frac{2}{5}q-\frac{2}{5}.\frac{11}{16}& \text{Uitwerken } \\ & =pq+\frac{11}{16}p-\frac{2}{5}q-\frac{22}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{11}{16}p-\frac{2}{5}q-\frac{11}{40} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{12}{19}+p)(a+\frac{11}{5})& =(\color{red}{p}+\color{orange}{\frac{12}{19}}).(\color{green}{a}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{12}{19})} . \color{green}{(a)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{11}{5}p+\frac{12}{19}a+\frac{12}{19}.\frac{11}{5}& \text{Uitwerken } \\ & =ap+\frac{11}{5}p+\frac{12}{19}a+\frac{132}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{2}{9})((-10)-b)& =(\color{red}{b}+\color{orange}{\frac{-2}{9}}).(\color{green}{-b}+\color{blue}{(-10)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(-10)} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -bb-10b+\frac{2}{9}b+\frac{2}{9}.10& \text{Uitwerken } \\ & =-b^2+((-10)+\frac{2}{9})b+(\frac{-20}{9}) & \text{Neem samen} \\ &=-b^2-\frac{88}{9}b+(\frac{-20}{9}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-14}{12})((-1)-b)& =(\color{red}{p}+\color{orange}{\frac{7}{6}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{7}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1p-\frac{7}{6}b-\frac{7}{6}.1& \text{Uitwerken } \\ & =-bp-1p-\frac{7}{6}b-\frac{7}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{6}{20})(\frac{6}{13}+q)& =(\color{red}{x}+\color{orange}{\frac{-3}{10}}).(\color{green}{q}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{6}{13}x-\frac{3}{10}q-\frac{3}{10}.\frac{6}{13}& \text{Uitwerken } \\ & =qx+\frac{6}{13}x-\frac{3}{10}q-\frac{18}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{6}{13}x-\frac{3}{10}q-\frac{9}{65} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-19}{19}+q)(q-\frac{-15}{3})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = qq+5q-1q-1.5& \text{Uitwerken } \\ & =q^2+(5+(-1))q-(-5) & \text{Neem samen} \\ &=q^2+4q-(-5) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-4}{10}+b)(a-\frac{15}{19})& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{19}b-\frac{2}{5}a+\frac{2}{5}.\frac{15}{19}& \text{Uitwerken } \\ & =ab-\frac{15}{19}b-\frac{2}{5}a+\frac{30}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{15}{19}b-\frac{2}{5}a+\frac{6}{19} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-1}{5})(x-5)& =(\color{red}{b}+\color{orange}{\frac{-1}{5}}).(\color{green}{x}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-5)} + \color{orange}{(\frac{-1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = bx-5b-\frac{1}{5}x+\frac{1}{5}.5& \text{Uitwerken } \\ & =bx-5b-\frac{1}{5}x+\frac{5}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-5b-\frac{1}{5}x+1 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(14+x)(a+\frac{-16}{10})& =(\color{red}{x}+\color{orange}{14}).(\color{green}{a}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(14)} . \color{green}{(a)} + \color{orange}{(14)} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{8}{5}x+14a-14.\frac{8}{5}& \text{Uitwerken } \\ & =ax-\frac{8}{5}x+14a-\frac{112}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-3}{9})(b+\frac{-8}{5})& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{5}q-\frac{1}{3}b+\frac{1}{3}.\frac{8}{5}& \text{Uitwerken } \\ & =bq-\frac{8}{5}q-\frac{1}{3}b+\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-12}{19}-a)(\frac{-15}{10}-a)& =(\color{red}{-a}+\color{orange}{\frac{-12}{19}}).(\color{green}{-a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{2}a+\frac{12}{19}a+\frac{12}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =a^2+(\frac{3}{2}+\frac{12}{19})a+\frac{36}{38} & \text{Neem samen} \\ &=a^2+\frac{81}{38}a+\frac{36}{38} & \text{Maak de som} \\ &=a^2+\frac{81}{38}a+\frac{18}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{6}{14}-x)(\frac{20}{11}-b)& =(\color{red}{-x}+\color{orange}{\frac{3}{7}}).(\color{green}{-b}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{3}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{20}{11}x-\frac{3}{7}b+\frac{3}{7}.\frac{20}{11}& \text{Uitwerken } \\ & =bx-\frac{20}{11}x-\frac{3}{7}b+\frac{60}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-18 00:19:34
Een site van Busleyden Atheneum Mechelen