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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-12}{9}-x)(p+\frac{-6}{9})& =(\color{red}{-x}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{3}x-\frac{4}{3}p+\frac{4}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-px+\frac{2}{3}x-\frac{4}{3}p+\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{3}{7})(\frac{-8}{19}-q)& =(\color{red}{x}+\color{orange}{\frac{-3}{7}}).(\color{green}{-q}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{8}{19}x+\frac{3}{7}q+\frac{3}{7}.\frac{8}{19}& \text{Uitwerken } \\ & =-qx-\frac{8}{19}x+\frac{3}{7}q+\frac{24}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{2}{16}+p)(p-\frac{3}{17})& =(\color{red}{p}+\color{orange}{\frac{1}{8}}).(\color{green}{p}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(\frac{1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{17}p+\frac{1}{8}p-\frac{1}{8}.\frac{3}{17}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{17})+\frac{1}{8})p-(\frac{-3}{136}) & \text{Neem samen} \\ &=p^2-\frac{7}{136}p-(\frac{-3}{136}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-8}{20})(a-\frac{18}{20})& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{10}b-\frac{2}{5}a+\frac{2}{5}.\frac{9}{10}& \text{Uitwerken } \\ & =ab-\frac{9}{10}b-\frac{2}{5}a+\frac{18}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{9}{10}b-\frac{2}{5}a+\frac{9}{25} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{14}{12}-b)(\frac{4}{18}-b)& =(\color{red}{-b}+\color{orange}{\frac{7}{6}}).(\color{green}{-b}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{7}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{2}{9}b-\frac{7}{6}b+\frac{7}{6}.\frac{2}{9}& \text{Uitwerken } \\ & =b^2+((\frac{-2}{9})+(\frac{-7}{6}))b+\frac{14}{54} & \text{Neem samen} \\ &=b^2-\frac{25}{18}b+\frac{14}{54} & \text{Maak de som} \\ &=b^2-\frac{25}{18}b+\frac{7}{27} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-17}{18})(\frac{18}{2}-b)& =(\color{red}{x}+\color{orange}{\frac{-17}{18}}).(\color{green}{-b}+\color{blue}{9})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(9)} + \color{orange}{(\frac{-17}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = -bx+9x+\frac{17}{18}b-\frac{17}{18}.9& \text{Uitwerken } \\ & =-bx+9x+\frac{17}{18}b-\frac{153}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+9x+\frac{17}{18}b-\frac{17}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{20}{7})(\frac{-13}{11}-q)& =(\color{red}{x}+\color{orange}{\frac{-20}{7}}).(\color{green}{-q}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{11}x+\frac{20}{7}q+\frac{20}{7}.\frac{13}{11}& \text{Uitwerken } \\ & =-qx-\frac{13}{11}x+\frac{20}{7}q+\frac{260}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-1)(\frac{-4}{10}+b)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{5}x-1b+1.\frac{2}{5}& \text{Uitwerken } \\ & =bx-\frac{2}{5}x-1b+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-12}{18}+p)(p+\frac{-7}{10})& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{7}{10}p-\frac{2}{3}p+\frac{2}{3}.\frac{7}{10}& \text{Uitwerken } \\ & =p^2+((\frac{-7}{10})+(\frac{-2}{3}))p+\frac{14}{30} & \text{Neem samen} \\ &=p^2-\frac{41}{30}p+\frac{14}{30} & \text{Maak de som} \\ &=p^2-\frac{41}{30}p+\frac{7}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-2}{6})(x+\frac{15}{11})& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{x}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{11}b-\frac{1}{3}x-\frac{1}{3}.\frac{15}{11}& \text{Uitwerken } \\ & =bx+\frac{15}{11}b-\frac{1}{3}x-\frac{15}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{15}{11}b-\frac{1}{3}x-\frac{5}{11} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{13}{2}+p)(a-\frac{5}{7})& =(\color{red}{p}+\color{orange}{\frac{13}{2}}).(\color{green}{a}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{13}{2})} . \color{green}{(a)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{7}p+\frac{13}{2}a-\frac{13}{2}.\frac{5}{7}& \text{Uitwerken } \\ & =ap-\frac{5}{7}p+\frac{13}{2}a-\frac{65}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(8-x)(\frac{17}{4}-b)& =(\color{red}{-x}+\color{orange}{8}).(\color{green}{-b}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(8)} . \color{green}{(-b)} + \color{orange}{(8)} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{4}x-8b+8.\frac{17}{4}& \text{Uitwerken } \\ & =bx-\frac{17}{4}x-8b+\frac{136}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{17}{4}x-8b+34 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-05 06:12:37
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