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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{4}+p)(\frac{-20}{4}-p)& =(\color{red}{p}+\color{orange}{\frac{15}{4}}).(\color{green}{-p}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(\frac{15}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -pp-5p-\frac{15}{4}p-\frac{15}{4}.5& \text{Uitwerken } \\ & =-p^2+((-5)+(\frac{-15}{4}))p-\frac{75}{4} & \text{Neem samen} \\ &=-p^2-\frac{35}{4}p-\frac{75}{4} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-4}{4})(\frac{7}{14}-p)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{2}a+1p-1.\frac{1}{2}& \text{Uitwerken } \\ & =-ap+\frac{1}{2}a+1p-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{4}{11}+x)(\frac{-7}{10}+x)& =(\color{red}{x}+\color{orange}{\frac{4}{11}}).(\color{green}{x}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{4}{11})} . \color{green}{(x)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{7}{10}x+\frac{4}{11}x-\frac{4}{11}.\frac{7}{10}& \text{Uitwerken } \\ & =x^2+((\frac{-7}{10})+\frac{4}{11})x-(\frac{-28}{110}) & \text{Neem samen} \\ &=x^2-\frac{37}{110}x-(\frac{-28}{110}) & \text{Maak de som} \\ &=x^2-\frac{37}{110}x+\frac{14}{55} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(\frac{1}{10}+a)(\frac{3}{7}+x)& =(\color{red}{a}+\color{orange}{\frac{1}{10}}).(\color{green}{x}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{7}a+\frac{1}{10}x+\frac{1}{10}.\frac{3}{7}& \text{Uitwerken } \\ & =ax+\frac{3}{7}a+\frac{1}{10}x+\frac{3}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{7}{16}-q)(q-\frac{-19}{4})& =(\color{red}{-q}+\color{orange}{\frac{7}{16}}).(\color{green}{q}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{7}{16})} . \color{green}{(q)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{19}{4}q+\frac{7}{16}q+\frac{7}{16}.\frac{19}{4}& \text{Uitwerken } \\ & =-q^2+((\frac{-19}{4})+\frac{7}{16})q+(\frac{-133}{64}) & \text{Neem samen} \\ &=-q^2-\frac{69}{16}q+(\frac{-133}{64}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-5}{12}-q)(\frac{19}{15}-x)& =(\color{red}{-q}+\color{orange}{\frac{-5}{12}}).(\color{green}{-x}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{-5}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{12})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{15}q+\frac{5}{12}x-\frac{5}{12}.\frac{19}{15}& \text{Uitwerken } \\ & =qx-\frac{19}{15}q+\frac{5}{12}x-\frac{95}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{19}{15}q+\frac{5}{12}x-\frac{19}{36} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-17}{3}+p)(p-\frac{17}{16})& =(\color{red}{p}+\color{orange}{\frac{-17}{3}}).(\color{green}{p}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{16}p-\frac{17}{3}p+\frac{17}{3}.\frac{17}{16}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{16})+(\frac{-17}{3}))p+\frac{289}{48} & \text{Neem samen} \\ &=p^2-\frac{323}{48}p+\frac{289}{48} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(q-(-9))(b+\frac{6}{12})& =(\color{red}{q}+\color{orange}{9}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(9)} . \color{green}{(b)} + \color{orange}{(9)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{2}q+9b+9.\frac{1}{2}& \text{Uitwerken } \\ & =bq+\frac{1}{2}q+9b+\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{-14}{13})(\frac{15}{14}-b)& =(\color{red}{q}+\color{orange}{\frac{-14}{13}}).(\color{green}{-b}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{15}{14}q+\frac{14}{13}b-\frac{14}{13}.\frac{15}{14}& \text{Uitwerken } \\ & =-bq+\frac{15}{14}q+\frac{14}{13}b-\frac{210}{182} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{15}{14}q+\frac{14}{13}b-\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b+\frac{3}{15})(b+\frac{-14}{16})& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{b}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{7}{8}b+\frac{1}{5}b-\frac{1}{5}.\frac{7}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-7}{8})+\frac{1}{5})b-(\frac{-7}{40}) & \text{Neem samen} \\ &=b^2-\frac{27}{40}b-(\frac{-7}{40}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-9}{13}+b)(q+\frac{-10}{16})& =(\color{red}{b}+\color{orange}{\frac{-9}{13}}).(\color{green}{q}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{8}b-\frac{9}{13}q+\frac{9}{13}.\frac{5}{8}& \text{Uitwerken } \\ & =bq-\frac{5}{8}b-\frac{9}{13}q+\frac{45}{104} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p+\frac{12}{17})(q+\frac{2}{7})& =(\color{red}{p}+\color{orange}{\frac{12}{17}}).(\color{green}{q}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{12}{17})} . \color{green}{(q)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{7}p+\frac{12}{17}q+\frac{12}{17}.\frac{2}{7}& \text{Uitwerken } \\ & =pq+\frac{2}{7}p+\frac{12}{17}q+\frac{24}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-01 17:14:49
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