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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{18}+x)(\frac{6}{4}-b)& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{-b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{2}x-\frac{1}{2}b+\frac{1}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =-bx+\frac{3}{2}x-\frac{1}{2}b+\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{13}{8})(\frac{-8}{4}+p)& =(\color{red}{p}+\color{orange}{\frac{13}{8}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{13}{8})} . \color{green}{(p)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pp-2p+\frac{13}{8}p-\frac{13}{8}.2& \text{Uitwerken } \\ & =p^2+((-2)+\frac{13}{8})p-(\frac{-26}{8}) & \text{Neem samen} \\ &=p^2-\frac{3}{8}p-(\frac{-26}{8}) & \text{Maak de som} \\ &=p^2-\frac{3}{8}p+\frac{13}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{18}-a)(p+\frac{10}{14})& =(\color{red}{-a}+\color{orange}{\frac{-8}{9}}).(\color{green}{p}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{7}a-\frac{8}{9}p-\frac{8}{9}.\frac{5}{7}& \text{Uitwerken } \\ & =-ap-\frac{5}{7}a-\frac{8}{9}p-\frac{40}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-14}{17})((-9)-a)& =(\color{red}{a}+\color{orange}{\frac{-14}{17}}).(\color{green}{-a}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(-9)} + \color{orange}{(\frac{-14}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -aa-9a+\frac{14}{17}a+\frac{14}{17}.9& \text{Uitwerken } \\ & =-a^2+((-9)+\frac{14}{17})a+(\frac{-126}{17}) & \text{Neem samen} \\ &=-a^2-\frac{139}{17}a+(\frac{-126}{17}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{18}{6}+x)(\frac{-8}{5}+a)& =(\color{red}{x}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{8}{5}x+3a-3.\frac{8}{5}& \text{Uitwerken } \\ & =ax-\frac{8}{5}x+3a-\frac{24}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{17}{12})(a-\frac{6}{11})& =(\color{red}{b}+\color{orange}{\frac{17}{12}}).(\color{green}{a}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{17}{12})} . \color{green}{(a)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{6}{11}b+\frac{17}{12}a-\frac{17}{12}.\frac{6}{11}& \text{Uitwerken } \\ & =ab-\frac{6}{11}b+\frac{17}{12}a-\frac{102}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{6}{11}b+\frac{17}{12}a-\frac{17}{22} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{17}-p)(x-\frac{-17}{10})& =(\color{red}{-p}+\color{orange}{\frac{8}{17}}).(\color{green}{x}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{8}{17})} . \color{green}{(x)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{17}{10}p+\frac{8}{17}x+\frac{8}{17}.\frac{17}{10}& \text{Uitwerken } \\ & =-px-\frac{17}{10}p+\frac{8}{17}x+\frac{136}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{17}{10}p+\frac{8}{17}x+\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-5}{10})(a-\frac{-16}{14})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{7}p+\frac{1}{2}a+\frac{1}{2}.\frac{8}{7}& \text{Uitwerken } \\ & =ap+\frac{8}{7}p+\frac{1}{2}a+\frac{8}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{8}{7}p+\frac{1}{2}a+\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{10}+q)(\frac{6}{11}+a)& =(\color{red}{q}+\color{orange}{\frac{-19}{10}}).(\color{green}{a}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{-19}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{11}q-\frac{19}{10}a-\frac{19}{10}.\frac{6}{11}& \text{Uitwerken } \\ & =aq+\frac{6}{11}q-\frac{19}{10}a-\frac{114}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{6}{11}q-\frac{19}{10}a-\frac{57}{55} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{20}{7})(x-\frac{15}{2})& =(\color{red}{q}+\color{orange}{\frac{-20}{7}}).(\color{green}{x}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{15}{2}q-\frac{20}{7}x+\frac{20}{7}.\frac{15}{2}& \text{Uitwerken } \\ & =qx-\frac{15}{2}q-\frac{20}{7}x+\frac{300}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{15}{2}q-\frac{20}{7}x+\frac{150}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-8}{14})(\frac{13}{17}+p)& =(\color{red}{q}+\color{orange}{\frac{-4}{7}}).(\color{green}{p}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{13}{17}q-\frac{4}{7}p-\frac{4}{7}.\frac{13}{17}& \text{Uitwerken } \\ & =pq+\frac{13}{17}q-\frac{4}{7}p-\frac{52}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-10}{10})(b+\frac{-8}{9})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{8}{9}a-1b+1.\frac{8}{9}& \text{Uitwerken } \\ & =ab-\frac{8}{9}a-1b+\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-24 17:28:41
Een site van Busleyden Atheneum Mechelen