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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{8}{20}+a)(\frac{20}{14}-p)& =(\color{red}{a}+\color{orange}{\frac{2}{5}}).(\color{green}{-p}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{10}{7}a-\frac{2}{5}p+\frac{2}{5}.\frac{10}{7}& \text{Uitwerken } \\ & =-ap+\frac{10}{7}a-\frac{2}{5}p+\frac{20}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{10}{7}a-\frac{2}{5}p+\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-20}{7})(x-\frac{17}{19})& =(\color{red}{b}+\color{orange}{\frac{-20}{7}}).(\color{green}{x}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{19}b-\frac{20}{7}x+\frac{20}{7}.\frac{17}{19}& \text{Uitwerken } \\ & =bx-\frac{17}{19}b-\frac{20}{7}x+\frac{340}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{4}{7}-b)(p+\frac{-6}{3})& =(\color{red}{-b}+\color{orange}{\frac{4}{7}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-2)} + \color{orange}{(\frac{4}{7})} . \color{green}{(p)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bp+2b+\frac{4}{7}p-\frac{4}{7}.2& \text{Uitwerken } \\ & =-bp+2b+\frac{4}{7}p-\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{1}{20})(x-\frac{-2}{17})& =(\color{red}{b}+\color{orange}{\frac{1}{20}}).(\color{green}{x}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{1}{20})} . \color{green}{(x)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{17}b+\frac{1}{20}x+\frac{1}{20}.\frac{2}{17}& \text{Uitwerken } \\ & =bx+\frac{2}{17}b+\frac{1}{20}x+\frac{2}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{2}{17}b+\frac{1}{20}x+\frac{1}{170} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x+(-5))(\frac{-2}{5}-q)& =(\color{red}{x}+\color{orange}{(-5)}).(\color{green}{-q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(-5)} . \color{green}{(-q)} + \color{orange}{(-5)} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{5}x+5q+5.\frac{2}{5}& \text{Uitwerken } \\ & =-qx-\frac{2}{5}x+5q+\frac{10}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{2}{5}x+5q+2 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-5}{3})(\frac{-10}{2}+a)& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-5)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = ax-5x-\frac{5}{3}a+\frac{5}{3}.5& \text{Uitwerken } \\ & =ax-5x-\frac{5}{3}a+\frac{25}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-11}{13}-q)(x-1)& =(\color{red}{-q}+\color{orange}{\frac{-11}{13}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-11}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1q-\frac{11}{13}x+\frac{11}{13}.1& \text{Uitwerken } \\ & =-qx+1q-\frac{11}{13}x+\frac{11}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{17}{4}-q)(\frac{19}{6}+p)& =(\color{red}{-q}+\color{orange}{\frac{17}{4}}).(\color{green}{p}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{17}{4})} . \color{green}{(p)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{6}q+\frac{17}{4}p+\frac{17}{4}.\frac{19}{6}& \text{Uitwerken } \\ & =-pq-\frac{19}{6}q+\frac{17}{4}p+\frac{323}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{11}{3}+b)(\frac{-15}{12}-b)& =(\color{red}{b}+\color{orange}{\frac{11}{3}}).(\color{green}{-b}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{11}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{5}{4}b-\frac{11}{3}b-\frac{11}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =-b^2+((\frac{-5}{4})+(\frac{-11}{3}))b-\frac{55}{12} & \text{Neem samen} \\ &=-b^2-\frac{59}{12}b-\frac{55}{12} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{13}{7}-a)(\frac{-16}{11}-b)& =(\color{red}{-a}+\color{orange}{\frac{13}{7}}).(\color{green}{-b}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{13}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{16}{11}a-\frac{13}{7}b-\frac{13}{7}.\frac{16}{11}& \text{Uitwerken } \\ & =ab+\frac{16}{11}a-\frac{13}{7}b-\frac{208}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{8}{14}-q)(a+\frac{19}{14})& =(\color{red}{-q}+\color{orange}{\frac{4}{7}}).(\color{green}{a}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{14}q+\frac{4}{7}a+\frac{4}{7}.\frac{19}{14}& \text{Uitwerken } \\ & =-aq-\frac{19}{14}q+\frac{4}{7}a+\frac{76}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{19}{14}q+\frac{4}{7}a+\frac{38}{49} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x+\frac{8}{10})(p-\frac{-19}{15})& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{19}{15}x+\frac{4}{5}p+\frac{4}{5}.\frac{19}{15}& \text{Uitwerken } \\ & =px+\frac{19}{15}x+\frac{4}{5}p+\frac{76}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-09 15:04:49
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