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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-9}{7}+b)(b-\frac{8}{9})& =(\color{red}{b}+\color{orange}{\frac{-9}{7}}).(\color{green}{b}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{8}{9}b-\frac{9}{7}b+\frac{9}{7}.\frac{8}{9}& \text{Uitwerken } \\ & =b^2+((\frac{-8}{9})+(\frac{-9}{7}))b+\frac{72}{63} & \text{Neem samen} \\ &=b^2-\frac{137}{63}b+\frac{72}{63} & \text{Maak de som} \\ &=b^2-\frac{137}{63}b+\frac{8}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(p-\frac{15}{2})(\frac{20}{3}-q)& =(\color{red}{p}+\color{orange}{\frac{-15}{2}}).(\color{green}{-q}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{20}{3}p+\frac{15}{2}q-\frac{15}{2}.\frac{20}{3}& \text{Uitwerken } \\ & =-pq+\frac{20}{3}p+\frac{15}{2}q-\frac{300}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{20}{3}p+\frac{15}{2}q-50 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{19}{13}+a)(p+\frac{19}{15})& =(\color{red}{a}+\color{orange}{\frac{19}{13}}).(\color{green}{p}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{19}{13})} . \color{green}{(p)} + \color{orange}{(\frac{19}{13})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{15}a+\frac{19}{13}p+\frac{19}{13}.\frac{19}{15}& \text{Uitwerken } \\ & =ap+\frac{19}{15}a+\frac{19}{13}p+\frac{361}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-4}{10}-p)(q+\frac{-11}{3})& =(\color{red}{-p}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{3}p-\frac{2}{5}q+\frac{2}{5}.\frac{11}{3}& \text{Uitwerken } \\ & =-pq+\frac{11}{3}p-\frac{2}{5}q+\frac{22}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{13}{20})(\frac{14}{14}+q)& =(\color{red}{a}+\color{orange}{\frac{13}{20}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{13}{20})} . \color{green}{(q)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aq+1a+\frac{13}{20}q+\frac{13}{20}.1& \text{Uitwerken } \\ & =aq+1a+\frac{13}{20}q+\frac{13}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{12}{16})(\frac{15}{14}-p)& =(\color{red}{a}+\color{orange}{\frac{-3}{4}}).(\color{green}{-p}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{15}{14}a+\frac{3}{4}p-\frac{3}{4}.\frac{15}{14}& \text{Uitwerken } \\ & =-ap+\frac{15}{14}a+\frac{3}{4}p-\frac{45}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{19}{12}-b)(\frac{1}{2}+a)& =(\color{red}{-b}+\color{orange}{\frac{19}{12}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{19}{12})} . \color{green}{(a)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{2}b+\frac{19}{12}a+\frac{19}{12}.\frac{1}{2}& \text{Uitwerken } \\ & =-ab-\frac{1}{2}b+\frac{19}{12}a+\frac{19}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{14}{18})(x+\frac{-3}{9})& =(\color{red}{a}+\color{orange}{\frac{-7}{9}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{3}a-\frac{7}{9}x+\frac{7}{9}.\frac{1}{3}& \text{Uitwerken } \\ & =ax-\frac{1}{3}a-\frac{7}{9}x+\frac{7}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-18}{15})(x-\frac{3}{9})& =(\color{red}{p}+\color{orange}{\frac{6}{5}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{3}p+\frac{6}{5}x-\frac{6}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =px-\frac{1}{3}p+\frac{6}{5}x-\frac{6}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{1}{3}p+\frac{6}{5}x-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-2}{17})(x+\frac{18}{10})& =(\color{red}{b}+\color{orange}{\frac{2}{17}}).(\color{green}{x}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{2}{17})} . \color{green}{(x)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{5}b+\frac{2}{17}x+\frac{2}{17}.\frac{9}{5}& \text{Uitwerken } \\ & =bx+\frac{9}{5}b+\frac{2}{17}x+\frac{18}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-17}{2})(\frac{-8}{19}-p)& =(\color{red}{q}+\color{orange}{\frac{17}{2}}).(\color{green}{-p}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{17}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{8}{19}q-\frac{17}{2}p-\frac{17}{2}.\frac{8}{19}& \text{Uitwerken } \\ & =-pq-\frac{8}{19}q-\frac{17}{2}p-\frac{136}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{8}{19}q-\frac{17}{2}p-\frac{68}{19} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{16}{2}-x)(p-\frac{-19}{11})& =(\color{red}{-x}+\color{orange}{8}).(\color{green}{p}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(8)} . \color{green}{(p)} + \color{orange}{(8)} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{11}x+8p+8.\frac{19}{11}& \text{Uitwerken } \\ & =-px-\frac{19}{11}x+8p+\frac{152}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-12 17:45:47
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