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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{7}{2}-q)(\frac{-2}{14}-q)& =(\color{red}{-q}+\color{orange}{\frac{7}{2}}).(\color{green}{-q}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{7}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{7}q-\frac{7}{2}q-\frac{7}{2}.\frac{1}{7}& \text{Uitwerken } \\ & =q^2+(\frac{1}{7}+(\frac{-7}{2}))q-(\frac{-7}{14}) & \text{Neem samen} \\ &=q^2-\frac{47}{14}q-(\frac{-7}{14}) & \text{Maak de som} \\ &=q^2-\frac{47}{14}q+\frac{1}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-3}{9})(x-\frac{-19}{11})& =(\color{red}{a}+\color{orange}{\frac{-1}{3}}).(\color{green}{x}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{11}a-\frac{1}{3}x-\frac{1}{3}.\frac{19}{11}& \text{Uitwerken } \\ & =ax+\frac{19}{11}a-\frac{1}{3}x-\frac{19}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-9}{8})(b-(-11))& =(\color{red}{b}+\color{orange}{\frac{-9}{8}}).(\color{green}{b}+\color{blue}{11})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(11)} + \color{orange}{(\frac{-9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = bb+11b-\frac{9}{8}b-\frac{9}{8}.11& \text{Uitwerken } \\ & =b^2+(11+(\frac{-9}{8}))b-(\frac{-99}{8}) & \text{Neem samen} \\ &=b^2+\frac{79}{8}b-(\frac{-99}{8}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(q+(-3))(q-\frac{-11}{20})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{q}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(-3)} . \color{green}{(q)} + \color{orange}{(-3)} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{11}{20}q-3q-3.\frac{11}{20}& \text{Uitwerken } \\ & =q^2+(\frac{11}{20}+(-3))q-(\frac{-33}{20}) & \text{Neem samen} \\ &=q^2-\frac{49}{20}q-(\frac{-33}{20}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{3}-q)(\frac{-14}{4}+q)& =(\color{red}{-q}+\color{orange}{(-5)}).(\color{green}{q}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(-5)} . \color{green}{(q)} + \color{orange}{(-5)} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{7}{2}q-5q+5.\frac{7}{2}& \text{Uitwerken } \\ & =-q^2+(\frac{7}{2}+(-5))q+(\frac{-35}{2}) & \text{Neem samen} \\ &=-q^2-\frac{3}{2}q+(\frac{-35}{2}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(p-\frac{18}{15})(a+\frac{2}{20})& =(\color{red}{p}+\color{orange}{\frac{-6}{5}}).(\color{green}{a}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{10}p-\frac{6}{5}a-\frac{6}{5}.\frac{1}{10}& \text{Uitwerken } \\ & =ap+\frac{1}{10}p-\frac{6}{5}a-\frac{6}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{10}p-\frac{6}{5}a-\frac{3}{25} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-13}{12})(b-\frac{19}{15})& =(\color{red}{x}+\color{orange}{\frac{13}{12}}).(\color{green}{b}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{13}{12})} . \color{green}{(b)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{15}x+\frac{13}{12}b-\frac{13}{12}.\frac{19}{15}& \text{Uitwerken } \\ & =bx-\frac{19}{15}x+\frac{13}{12}b-\frac{247}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-14}{8}+x)(\frac{-1}{10}-q)& =(\color{red}{x}+\color{orange}{\frac{-7}{4}}).(\color{green}{-q}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{10}x+\frac{7}{4}q+\frac{7}{4}.\frac{1}{10}& \text{Uitwerken } \\ & =-qx-\frac{1}{10}x+\frac{7}{4}q+\frac{7}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{20}{18})(\frac{-15}{12}-a)& =(\color{red}{q}+\color{orange}{\frac{-10}{9}}).(\color{green}{-a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{4}q+\frac{10}{9}a+\frac{10}{9}.\frac{5}{4}& \text{Uitwerken } \\ & =-aq-\frac{5}{4}q+\frac{10}{9}a+\frac{50}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{5}{4}q+\frac{10}{9}a+\frac{25}{18} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-14}{16}-p)(\frac{4}{17}+p)& =(\color{red}{-p}+\color{orange}{\frac{-7}{8}}).(\color{green}{p}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{4}{17}p-\frac{7}{8}p-\frac{7}{8}.\frac{4}{17}& \text{Uitwerken } \\ & =-p^2+((\frac{-4}{17})+(\frac{-7}{8}))p-\frac{28}{136} & \text{Neem samen} \\ &=-p^2-\frac{151}{136}p-\frac{28}{136} & \text{Maak de som} \\ &=-p^2-\frac{151}{136}p-\frac{7}{34} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(a-\frac{3}{20})(\frac{-14}{4}-p)& =(\color{red}{a}+\color{orange}{\frac{-3}{20}}).(\color{green}{-p}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{7}{2}a+\frac{3}{20}p+\frac{3}{20}.\frac{7}{2}& \text{Uitwerken } \\ & =-ap-\frac{7}{2}a+\frac{3}{20}p+\frac{21}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{17}{3}+x)(q+\frac{17}{18})& =(\color{red}{x}+\color{orange}{\frac{17}{3}}).(\color{green}{q}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{17}{3})} . \color{green}{(q)} + \color{orange}{(\frac{17}{3})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{18}x+\frac{17}{3}q+\frac{17}{3}.\frac{17}{18}& \text{Uitwerken } \\ & =qx+\frac{17}{18}x+\frac{17}{3}q+\frac{289}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-13 14:39:59
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