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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-7}{8})(a+4)& =(\color{red}{b}+\color{orange}{\frac{-7}{8}}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(4)} + \color{orange}{(\frac{-7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ab+4b-\frac{7}{8}a-\frac{7}{8}.4& \text{Uitwerken } \\ & =ab+4b-\frac{7}{8}a-\frac{28}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+4b-\frac{7}{8}a-\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-14}{18})(x-\frac{-4}{11})& =(\color{red}{a}+\color{orange}{\frac{-7}{9}}).(\color{green}{x}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{11}a-\frac{7}{9}x-\frac{7}{9}.\frac{4}{11}& \text{Uitwerken } \\ & =ax+\frac{4}{11}a-\frac{7}{9}x-\frac{28}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{20}{7}+p)(a-11)& =(\color{red}{p}+\color{orange}{\frac{20}{7}}).(\color{green}{a}+\color{blue}{(-11)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-11)} + \color{orange}{(\frac{20}{7})} . \color{green}{(a)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = ap-11p+\frac{20}{7}a-\frac{20}{7}.11& \text{Uitwerken } \\ & =ap-11p+\frac{20}{7}a-\frac{220}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{4}{14})(q-\frac{-14}{17})& =(\color{red}{a}+\color{orange}{\frac{2}{7}}).(\color{green}{q}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{2}{7})} . \color{green}{(q)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{14}{17}a+\frac{2}{7}q+\frac{2}{7}.\frac{14}{17}& \text{Uitwerken } \\ & =aq+\frac{14}{17}a+\frac{2}{7}q+\frac{28}{119} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{14}{17}a+\frac{2}{7}q+\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b+\frac{-20}{4})(x-\frac{-16}{11})& =(\color{red}{b}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{16}{11}b-5x-5.\frac{16}{11}& \text{Uitwerken } \\ & =bx+\frac{16}{11}b-5x-\frac{80}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{15}+b)(\frac{2}{11}-q)& =(\color{red}{b}+\color{orange}{\frac{4}{3}}).(\color{green}{-q}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{11}b-\frac{4}{3}q+\frac{4}{3}.\frac{2}{11}& \text{Uitwerken } \\ & =-bq+\frac{2}{11}b-\frac{4}{3}q+\frac{8}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-16}{2})(\frac{6}{15}+a)& =(\color{red}{q}+\color{orange}{8}).(\color{green}{a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(8)} . \color{green}{(a)} + \color{orange}{(8)} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{5}q+8a+8.\frac{2}{5}& \text{Uitwerken } \\ & =aq+\frac{2}{5}q+8a+\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-10}{2}-q)(\frac{-16}{15}+a)& =(\color{red}{-q}+\color{orange}{(-5)}).(\color{green}{a}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(-5)} . \color{green}{(a)} + \color{orange}{(-5)} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{16}{15}q-5a+5.\frac{16}{15}& \text{Uitwerken } \\ & =-aq+\frac{16}{15}q-5a+\frac{80}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{16}{15}q-5a+\frac{16}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{19}{17}-x)(x+\frac{-18}{10})& =(\color{red}{-x}+\color{orange}{\frac{19}{17}}).(\color{green}{x}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{19}{17})} . \color{green}{(x)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{9}{5}x+\frac{19}{17}x-\frac{19}{17}.\frac{9}{5}& \text{Uitwerken } \\ & =-x^2+(\frac{9}{5}+\frac{19}{17})x-\frac{171}{85} & \text{Neem samen} \\ &=-x^2+\frac{248}{85}x-\frac{171}{85} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-12}{4}-b)(\frac{1}{14}-b)& =(\color{red}{-b}+\color{orange}{(-3)}).(\color{green}{-b}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(-3)} . \color{green}{(-b)} + \color{orange}{(-3)} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{14}b+3b-3.\frac{1}{14}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{14})+3)b-(\frac{-3}{14}) & \text{Neem samen} \\ &=b^2+\frac{41}{14}b-(\frac{-3}{14}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(x+\frac{15}{3})(b-\frac{-15}{5})& =(\color{red}{x}+\color{orange}{5}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(5)} . \color{green}{(b)} + \color{orange}{(5)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bx+3x+5b+5.3& \text{Uitwerken } \\ & =bx+3x+5b+15 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-17}{3}-p)(a-\frac{14}{14})& =(\color{red}{-p}+\color{orange}{\frac{-17}{3}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-17}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1p-\frac{17}{3}a+\frac{17}{3}.1& \text{Uitwerken } \\ & =-ap+1p-\frac{17}{3}a+\frac{17}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-12 23:25:29
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