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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{4}{8})(p-\frac{11}{19})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{19}q-\frac{1}{2}p+\frac{1}{2}.\frac{11}{19}& \text{Uitwerken } \\ & =pq-\frac{11}{19}q-\frac{1}{2}p+\frac{11}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+(-8))(\frac{-20}{13}+x)& =(\color{red}{a}+\color{orange}{(-8)}).(\color{green}{x}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(-8)} . \color{green}{(x)} + \color{orange}{(-8)} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{20}{13}a-8x+8.\frac{20}{13}& \text{Uitwerken } \\ & =ax-\frac{20}{13}a-8x+\frac{160}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{17}{7})(\frac{-20}{3}-q)& =(\color{red}{q}+\color{orange}{\frac{-17}{7}}).(\color{green}{-q}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{-17}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{7})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{20}{3}q+\frac{17}{7}q+\frac{17}{7}.\frac{20}{3}& \text{Uitwerken } \\ & =-q^2+((\frac{-20}{3})+\frac{17}{7})q+(\frac{-340}{21}) & \text{Neem samen} \\ &=-q^2-\frac{89}{21}q+(\frac{-340}{21}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-18}{12})(\frac{-1}{12}-x)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{-x}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{12}b+\frac{3}{2}x+\frac{3}{2}.\frac{1}{12}& \text{Uitwerken } \\ & =-bx-\frac{1}{12}b+\frac{3}{2}x+\frac{3}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{1}{12}b+\frac{3}{2}x+\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{7}{17}-a)(\frac{19}{10}-q)& =(\color{red}{-a}+\color{orange}{\frac{7}{17}}).(\color{green}{-q}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{7}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{10}a-\frac{7}{17}q+\frac{7}{17}.\frac{19}{10}& \text{Uitwerken } \\ & =aq-\frac{19}{10}a-\frac{7}{17}q+\frac{133}{170} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{7}{18})(b+\frac{-20}{13})& =(\color{red}{q}+\color{orange}{\frac{-7}{18}}).(\color{green}{b}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{20}{13}q-\frac{7}{18}b+\frac{7}{18}.\frac{20}{13}& \text{Uitwerken } \\ & =bq-\frac{20}{13}q-\frac{7}{18}b+\frac{140}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{20}{13}q-\frac{7}{18}b+\frac{70}{117} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-18}{14})(q+\frac{4}{9})& =(\color{red}{b}+\color{orange}{\frac{-9}{7}}).(\color{green}{q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{9}b-\frac{9}{7}q-\frac{9}{7}.\frac{4}{9}& \text{Uitwerken } \\ & =bq+\frac{4}{9}b-\frac{9}{7}q-\frac{36}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{4}{9}b-\frac{9}{7}q-\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{13}-q)(\frac{-15}{7}+p)& =(\color{red}{-q}+\color{orange}{\frac{18}{13}}).(\color{green}{p}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{18}{13})} . \color{green}{(p)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{15}{7}q+\frac{18}{13}p-\frac{18}{13}.\frac{15}{7}& \text{Uitwerken } \\ & =-pq+\frac{15}{7}q+\frac{18}{13}p-\frac{270}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-5}{17})(\frac{4}{2}-p)& =(\color{red}{q}+\color{orange}{\frac{5}{17}}).(\color{green}{-p}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{5}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -pq+2q-\frac{5}{17}p+\frac{5}{17}.2& \text{Uitwerken } \\ & =-pq+2q-\frac{5}{17}p+\frac{10}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{9}{16})((-8)+x)& =(\color{red}{q}+\color{orange}{\frac{9}{16}}).(\color{green}{x}+\color{blue}{(-8)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-8)} + \color{orange}{(\frac{9}{16})} . \color{green}{(x)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = qx-8q+\frac{9}{16}x-\frac{9}{16}.8& \text{Uitwerken } \\ & =qx-8q+\frac{9}{16}x-\frac{72}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-8q+\frac{9}{16}x-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{14}-b)(x-\frac{-5}{15})& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{3}b+1x+1.\frac{1}{3}& \text{Uitwerken } \\ & =-bx-\frac{1}{3}b+1x+\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}((-16)+q)(p+\frac{5}{14})& =(\color{red}{q}+\color{orange}{(-16)}).(\color{green}{p}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(-16)} . \color{green}{(p)} + \color{orange}{(-16)} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{14}q-16p-16.\frac{5}{14}& \text{Uitwerken } \\ & =pq+\frac{5}{14}q-16p-\frac{80}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{5}{14}q-16p-\frac{40}{7} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-14 17:35:22
Een site van Busleyden Atheneum Mechelen