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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-20}{19})(\frac{-17}{10}-p)& =(\color{red}{a}+\color{orange}{\frac{20}{19}}).(\color{green}{-p}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{20}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{10}a-\frac{20}{19}p-\frac{20}{19}.\frac{17}{10}& \text{Uitwerken } \\ & =-ap-\frac{17}{10}a-\frac{20}{19}p-\frac{340}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{17}{10}a-\frac{20}{19}p-\frac{34}{19} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p-\frac{1}{13})(\frac{-18}{9}+q)& =(\color{red}{p}+\color{orange}{\frac{-1}{13}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-1}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq-2p-\frac{1}{13}q+\frac{1}{13}.2& \text{Uitwerken } \\ & =pq-2p-\frac{1}{13}q+\frac{2}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{18}{2})(\frac{18}{5}+q)& =(\color{red}{q}+\color{orange}{(-9)}).(\color{green}{q}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(-9)} . \color{green}{(q)} + \color{orange}{(-9)} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{18}{5}q-9q-9.\frac{18}{5}& \text{Uitwerken } \\ & =q^2+(\frac{18}{5}+(-9))q-(\frac{-162}{5}) & \text{Neem samen} \\ &=q^2-\frac{27}{5}q-(\frac{-162}{5}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-17}{7})(\frac{-13}{7}+b)& =(\color{red}{a}+\color{orange}{\frac{-17}{7}}).(\color{green}{b}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{-17}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{7})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{7}a-\frac{17}{7}b+\frac{17}{7}.\frac{13}{7}& \text{Uitwerken } \\ & =ab-\frac{13}{7}a-\frac{17}{7}b+\frac{221}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{18}{19})(a+\frac{-7}{7})& =(\color{red}{x}+\color{orange}{\frac{-18}{19}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-18}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x-\frac{18}{19}a+\frac{18}{19}.1& \text{Uitwerken } \\ & =ax-1x-\frac{18}{19}a+\frac{18}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-9}{6})(\frac{-3}{16}+p)& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{16}p+\frac{3}{2}p-\frac{3}{2}.\frac{3}{16}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{16})+\frac{3}{2})p-(\frac{-9}{32}) & \text{Neem samen} \\ &=p^2+\frac{21}{16}p-(\frac{-9}{32}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(q-\frac{4}{8})(b+\frac{1}{18})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{18}q-\frac{1}{2}b-\frac{1}{2}.\frac{1}{18}& \text{Uitwerken } \\ & =bq+\frac{1}{18}q-\frac{1}{2}b-\frac{1}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-5}{19})(\frac{19}{4}+q)& =(\color{red}{p}+\color{orange}{\frac{-5}{19}}).(\color{green}{q}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{19}{4}p-\frac{5}{19}q-\frac{5}{19}.\frac{19}{4}& \text{Uitwerken } \\ & =pq+\frac{19}{4}p-\frac{5}{19}q-\frac{95}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{19}{4}p-\frac{5}{19}q-\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-18}{2})(\frac{11}{6}+a)& =(\color{red}{x}+\color{orange}{(-9)}).(\color{green}{a}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(-9)} . \color{green}{(a)} + \color{orange}{(-9)} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{6}x-9a-9.\frac{11}{6}& \text{Uitwerken } \\ & =ax+\frac{11}{6}x-9a-\frac{99}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{11}{6}x-9a-\frac{33}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-8}{16})(a+\frac{-8}{4})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aa-2a-\frac{1}{2}a+\frac{1}{2}.2& \text{Uitwerken } \\ & =a^2+((-2)+(\frac{-1}{2}))a+\frac{2}{2} & \text{Neem samen} \\ &=a^2-\frac{5}{2}a+\frac{2}{2} & \text{Maak de som} \\ &=a^2-\frac{5}{2}a+1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-12}{2}+p)(a+\frac{17}{14})& =(\color{red}{p}+\color{orange}{(-6)}).(\color{green}{a}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(-6)} . \color{green}{(a)} + \color{orange}{(-6)} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{14}p-6a-6.\frac{17}{14}& \text{Uitwerken } \\ & =ap+\frac{17}{14}p-6a-\frac{102}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{17}{14}p-6a-\frac{51}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-11}{14})(\frac{-18}{17}-b)& =(\color{red}{q}+\color{orange}{\frac{-11}{14}}).(\color{green}{-b}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{18}{17}q+\frac{11}{14}b+\frac{11}{14}.\frac{18}{17}& \text{Uitwerken } \\ & =-bq-\frac{18}{17}q+\frac{11}{14}b+\frac{198}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{18}{17}q+\frac{11}{14}b+\frac{99}{119} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-06 09:22:21
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