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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{8}-x)(\frac{-19}{12}+q)& =(\color{red}{-x}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{19}{12}x+\frac{1}{2}q-\frac{1}{2}.\frac{19}{12}& \text{Uitwerken } \\ & =-qx+\frac{19}{12}x+\frac{1}{2}q-\frac{19}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-5}{14})(x+\frac{-19}{17})& =(\color{red}{b}+\color{orange}{\frac{5}{14}}).(\color{green}{x}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{5}{14})} . \color{green}{(x)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{17}b+\frac{5}{14}x-\frac{5}{14}.\frac{19}{17}& \text{Uitwerken } \\ & =bx-\frac{19}{17}b+\frac{5}{14}x-\frac{95}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-4}{10}+p)(\frac{3}{11}-p)& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{-p}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{3}{11})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{3}{11}p+\frac{2}{5}p-\frac{2}{5}.\frac{3}{11}& \text{Uitwerken } \\ & =-p^2+(\frac{3}{11}+\frac{2}{5})p-\frac{6}{55} & \text{Neem samen} \\ &=-p^2+\frac{37}{55}p-\frac{6}{55} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{16}{8}+q)(\frac{-15}{16}+a)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{16}q+2a-2.\frac{15}{16}& \text{Uitwerken } \\ & =aq-\frac{15}{16}q+2a-\frac{30}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{15}{16}q+2a-\frac{15}{8} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{6}{14}+q)(\frac{16}{18}-a)& =(\color{red}{q}+\color{orange}{\frac{3}{7}}).(\color{green}{-a}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{3}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{8}{9}q-\frac{3}{7}a+\frac{3}{7}.\frac{8}{9}& \text{Uitwerken } \\ & =-aq+\frac{8}{9}q-\frac{3}{7}a+\frac{24}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{8}{9}q-\frac{3}{7}a+\frac{8}{21} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-5}{7}-x)(x+\frac{7}{3})& =(\color{red}{-x}+\color{orange}{\frac{-5}{7}}).(\color{green}{x}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{7}{3}x-\frac{5}{7}x-\frac{5}{7}.\frac{7}{3}& \text{Uitwerken } \\ & =-x^2+((\frac{-7}{3})+(\frac{-5}{7}))x-\frac{35}{21} & \text{Neem samen} \\ &=-x^2-\frac{64}{21}x-\frac{35}{21} & \text{Maak de som} \\ &=-x^2-\frac{64}{21}x-\frac{5}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{17}{16}-p)(\frac{13}{20}+x)& =(\color{red}{-p}+\color{orange}{\frac{17}{16}}).(\color{green}{x}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{17}{16})} . \color{green}{(x)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{13}{20}p+\frac{17}{16}x+\frac{17}{16}.\frac{13}{20}& \text{Uitwerken } \\ & =-px-\frac{13}{20}p+\frac{17}{16}x+\frac{221}{320} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-14}{11})(q-\frac{4}{16})& =(\color{red}{a}+\color{orange}{\frac{14}{11}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{14}{11})} . \color{green}{(q)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{4}a+\frac{14}{11}q-\frac{14}{11}.\frac{1}{4}& \text{Uitwerken } \\ & =aq-\frac{1}{4}a+\frac{14}{11}q-\frac{14}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{4}a+\frac{14}{11}q-\frac{7}{22} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{9}{17})(\frac{-3}{5}-x)& =(\color{red}{p}+\color{orange}{\frac{-9}{17}}).(\color{green}{-x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{5}p+\frac{9}{17}x+\frac{9}{17}.\frac{3}{5}& \text{Uitwerken } \\ & =-px-\frac{3}{5}p+\frac{9}{17}x+\frac{27}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{3}{12})(p+\frac{-4}{15})& =(\color{red}{p}+\color{orange}{\frac{1}{4}}).(\color{green}{p}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{4}{15}p+\frac{1}{4}p-\frac{1}{4}.\frac{4}{15}& \text{Uitwerken } \\ & =p^2+((\frac{-4}{15})+\frac{1}{4})p-(\frac{-4}{60}) & \text{Neem samen} \\ &=p^2-\frac{1}{60}p-(\frac{-4}{60}) & \text{Maak de som} \\ &=p^2-\frac{1}{60}p+\frac{1}{15} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(b-\frac{14}{12})(\frac{5}{9}+q)& =(\color{red}{b}+\color{orange}{\frac{-7}{6}}).(\color{green}{q}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{9}b-\frac{7}{6}q-\frac{7}{6}.\frac{5}{9}& \text{Uitwerken } \\ & =bq+\frac{5}{9}b-\frac{7}{6}q-\frac{35}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-11}{8}+a)((-5)+q)& =(\color{red}{a}+\color{orange}{\frac{-11}{8}}).(\color{green}{q}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-5)} + \color{orange}{(\frac{-11}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = aq-5a-\frac{11}{8}q+\frac{11}{8}.5& \text{Uitwerken } \\ & =aq-5a-\frac{11}{8}q+\frac{55}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-02 20:09:44
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