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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-16}{13})(a-\frac{-7}{8})& =(\color{red}{q}+\color{orange}{\frac{16}{13}}).(\color{green}{a}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{16}{13})} . \color{green}{(a)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{8}q+\frac{16}{13}a+\frac{16}{13}.\frac{7}{8}& \text{Uitwerken } \\ & =aq+\frac{7}{8}q+\frac{16}{13}a+\frac{112}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{7}{8}q+\frac{16}{13}a+\frac{14}{13} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-4}{4}+q)(b-\frac{-17}{9})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{9}q-1b-1.\frac{17}{9}& \text{Uitwerken } \\ & =bq+\frac{17}{9}q-1b-\frac{17}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{14}{13}-p)(\frac{10}{18}-a)& =(\color{red}{-p}+\color{orange}{\frac{14}{13}}).(\color{green}{-a}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{14}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{9}p-\frac{14}{13}a+\frac{14}{13}.\frac{5}{9}& \text{Uitwerken } \\ & =ap-\frac{5}{9}p-\frac{14}{13}a+\frac{70}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-4}{16})(x-\frac{9}{5})& =(\color{red}{x}+\color{orange}{\frac{-1}{4}}).(\color{green}{x}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{9}{5}x-\frac{1}{4}x+\frac{1}{4}.\frac{9}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-9}{5})+(\frac{-1}{4}))x+\frac{9}{20} & \text{Neem samen} \\ &=x^2-\frac{41}{20}x+\frac{9}{20} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{5}+p)(q-\frac{-7}{16})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{16}p-2q-2.\frac{7}{16}& \text{Uitwerken } \\ & =pq+\frac{7}{16}p-2q-\frac{14}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{7}{16}p-2q-\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-4}{3})(\frac{18}{9}+q)& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bq+2b-\frac{4}{3}q-\frac{4}{3}.2& \text{Uitwerken } \\ & =bq+2b-\frac{4}{3}q-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{12}{19})(x-\frac{-19}{14})& =(\color{red}{q}+\color{orange}{\frac{-12}{19}}).(\color{green}{x}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{14}q-\frac{12}{19}x-\frac{12}{19}.\frac{19}{14}& \text{Uitwerken } \\ & =qx+\frac{19}{14}q-\frac{12}{19}x-\frac{228}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{19}{14}q-\frac{12}{19}x-\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x+\frac{2}{9})(p+\frac{13}{16})& =(\color{red}{x}+\color{orange}{\frac{2}{9}}).(\color{green}{p}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{2}{9})} . \color{green}{(p)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{16}x+\frac{2}{9}p+\frac{2}{9}.\frac{13}{16}& \text{Uitwerken } \\ & =px+\frac{13}{16}x+\frac{2}{9}p+\frac{26}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{13}{16}x+\frac{2}{9}p+\frac{13}{72} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{13}{9}-b)(\frac{-18}{11}+p)& =(\color{red}{-b}+\color{orange}{\frac{13}{9}}).(\color{green}{p}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{13}{9})} . \color{green}{(p)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{18}{11}b+\frac{13}{9}p-\frac{13}{9}.\frac{18}{11}& \text{Uitwerken } \\ & =-bp+\frac{18}{11}b+\frac{13}{9}p-\frac{234}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{18}{11}b+\frac{13}{9}p-\frac{26}{11} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+\frac{18}{2})(\frac{-13}{4}-a)& =(\color{red}{p}+\color{orange}{9}).(\color{green}{-a}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(9)} . \color{green}{(-a)} + \color{orange}{(9)} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{4}p-9a-9.\frac{13}{4}& \text{Uitwerken } \\ & =-ap-\frac{13}{4}p-9a-\frac{117}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{13}{3})(\frac{-18}{20}-b)& =(\color{red}{a}+\color{orange}{\frac{-13}{3}}).(\color{green}{-b}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-13}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{9}{10}a+\frac{13}{3}b+\frac{13}{3}.\frac{9}{10}& \text{Uitwerken } \\ & =-ab-\frac{9}{10}a+\frac{13}{3}b+\frac{117}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{9}{10}a+\frac{13}{3}b+\frac{39}{10} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p+\frac{17}{10})(\frac{-10}{10}+x)& =(\color{red}{p}+\color{orange}{\frac{17}{10}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{17}{10})} . \color{green}{(x)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1p+\frac{17}{10}x-\frac{17}{10}.1& \text{Uitwerken } \\ & =px-1p+\frac{17}{10}x-\frac{17}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-17 16:54:04
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