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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{20}+a)(\frac{-18}{8}-x)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{9}{4}a-1x-1.\frac{9}{4}& \text{Uitwerken } \\ & =-ax-\frac{9}{4}a-1x-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{9}{14})(\frac{19}{14}-b)& =(\color{red}{x}+\color{orange}{\frac{-9}{14}}).(\color{green}{-b}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{19}{14}x+\frac{9}{14}b-\frac{9}{14}.\frac{19}{14}& \text{Uitwerken } \\ & =-bx+\frac{19}{14}x+\frac{9}{14}b-\frac{171}{196} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-17}{13})(\frac{1}{14}+a)& =(\color{red}{p}+\color{orange}{\frac{17}{13}}).(\color{green}{a}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{17}{13})} . \color{green}{(a)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{14}p+\frac{17}{13}a+\frac{17}{13}.\frac{1}{14}& \text{Uitwerken } \\ & =ap+\frac{1}{14}p+\frac{17}{13}a+\frac{17}{182} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{10}{9}-b)(a+\frac{20}{18})& =(\color{red}{-b}+\color{orange}{\frac{10}{9}}).(\color{green}{a}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{10}{9}b+\frac{10}{9}a+\frac{10}{9}.\frac{10}{9}& \text{Uitwerken } \\ & =-ab-\frac{10}{9}b+\frac{10}{9}a+\frac{100}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{17}+p)(x-\frac{17}{18})& =(\color{red}{p}+\color{orange}{\frac{16}{17}}).(\color{green}{x}+\color{blue}{\frac{-17}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{18})} + \color{orange}{(\frac{16}{17})} . \color{green}{(x)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{-17}{18})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{18}p+\frac{16}{17}x-\frac{16}{17}.\frac{17}{18}& \text{Uitwerken } \\ & =px-\frac{17}{18}p+\frac{16}{17}x-\frac{272}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{17}{18}p+\frac{16}{17}x-\frac{8}{9} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-11}{11}+p)(x-\frac{-20}{6})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{10}{3}p-1x-1.\frac{10}{3}& \text{Uitwerken } \\ & =px+\frac{10}{3}p-1x-\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{9}{7})(\frac{-18}{9}-p)& =(\color{red}{p}+\color{orange}{\frac{9}{7}}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{9}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -pp-2p-\frac{9}{7}p-\frac{9}{7}.2& \text{Uitwerken } \\ & =-p^2+((-2)+(\frac{-9}{7}))p-\frac{18}{7} & \text{Neem samen} \\ &=-p^2-\frac{23}{7}p-\frac{18}{7} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(b-\frac{9}{7})(\frac{5}{16}+b)& =(\color{red}{b}+\color{orange}{\frac{-9}{7}}).(\color{green}{b}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{16}b-\frac{9}{7}b-\frac{9}{7}.\frac{5}{16}& \text{Uitwerken } \\ & =b^2+(\frac{5}{16}+(\frac{-9}{7}))b-(\frac{-45}{112}) & \text{Neem samen} \\ &=b^2-\frac{109}{112}b-(\frac{-45}{112}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-4}{15})(\frac{-10}{8}-x)& =(\color{red}{b}+\color{orange}{\frac{-4}{15}}).(\color{green}{-x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{4}b+\frac{4}{15}x+\frac{4}{15}.\frac{5}{4}& \text{Uitwerken } \\ & =-bx-\frac{5}{4}b+\frac{4}{15}x+\frac{20}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{5}{4}b+\frac{4}{15}x+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{14}{5})(\frac{3}{10}+a)& =(\color{red}{p}+\color{orange}{\frac{-14}{5}}).(\color{green}{a}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{10}p-\frac{14}{5}a-\frac{14}{5}.\frac{3}{10}& \text{Uitwerken } \\ & =ap+\frac{3}{10}p-\frac{14}{5}a-\frac{42}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{10}p-\frac{14}{5}a-\frac{21}{25} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{7}{12})(\frac{14}{15}+p)& =(\color{red}{x}+\color{orange}{\frac{7}{12}}).(\color{green}{p}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(\frac{7}{12})} . \color{green}{(p)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{14}{15}x+\frac{7}{12}p+\frac{7}{12}.\frac{14}{15}& \text{Uitwerken } \\ & =px+\frac{14}{15}x+\frac{7}{12}p+\frac{98}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{14}{15}x+\frac{7}{12}p+\frac{49}{90} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{6}{17}-a)(\frac{-8}{20}-x)& =(\color{red}{-a}+\color{orange}{\frac{6}{17}}).(\color{green}{-x}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{6}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{5}a-\frac{6}{17}x-\frac{6}{17}.\frac{2}{5}& \text{Uitwerken } \\ & =ax+\frac{2}{5}a-\frac{6}{17}x-\frac{12}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-24 16:02:10
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