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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{16}{14})(\frac{9}{20}+b)& =(\color{red}{b}+\color{orange}{\frac{8}{7}}).(\color{green}{b}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{8}{7})} . \color{green}{(b)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{9}{20}b+\frac{8}{7}b+\frac{8}{7}.\frac{9}{20}& \text{Uitwerken } \\ & =b^2+(\frac{9}{20}+\frac{8}{7})b+\frac{72}{140} & \text{Neem samen} \\ &=b^2+\frac{223}{140}b+\frac{72}{140} & \text{Maak de som} \\ &=b^2+\frac{223}{140}b+\frac{18}{35} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-2}{6}+x)(\frac{2}{2}-a)& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ax+1x+\frac{1}{3}a-\frac{1}{3}.1& \text{Uitwerken } \\ & =-ax+1x+\frac{1}{3}a-\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-18}{12})(\frac{-16}{4}-q)& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{-q}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(-4)} + \color{orange}{(\frac{3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -bq-4b-\frac{3}{2}q-\frac{3}{2}.4& \text{Uitwerken } \\ & =-bq-4b-\frac{3}{2}q-\frac{12}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-4b-\frac{3}{2}q-6 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{18}+p)(b+\frac{-11}{13})& =(\color{red}{p}+\color{orange}{\frac{11}{18}}).(\color{green}{b}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{11}{18})} . \color{green}{(b)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{13}p+\frac{11}{18}b-\frac{11}{18}.\frac{11}{13}& \text{Uitwerken } \\ & =bp-\frac{11}{13}p+\frac{11}{18}b-\frac{121}{234} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{9}-a)(x+\frac{-15}{11})& =(\color{red}{-a}+\color{orange}{\frac{-16}{9}}).(\color{green}{x}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{15}{11}a-\frac{16}{9}x+\frac{16}{9}.\frac{15}{11}& \text{Uitwerken } \\ & =-ax+\frac{15}{11}a-\frac{16}{9}x+\frac{240}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{15}{11}a-\frac{16}{9}x+\frac{80}{33} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{16}{9}+p)(x+\frac{-8}{17})& =(\color{red}{p}+\color{orange}{\frac{16}{9}}).(\color{green}{x}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{16}{9})} . \color{green}{(x)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{8}{17}p+\frac{16}{9}x-\frac{16}{9}.\frac{8}{17}& \text{Uitwerken } \\ & =px-\frac{8}{17}p+\frac{16}{9}x-\frac{128}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{11}-q)(\frac{20}{9}+b)& =(\color{red}{-q}+\color{orange}{\frac{9}{11}}).(\color{green}{b}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{9}{11})} . \color{green}{(b)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{20}{9}q+\frac{9}{11}b+\frac{9}{11}.\frac{20}{9}& \text{Uitwerken } \\ & =-bq-\frac{20}{9}q+\frac{9}{11}b+\frac{180}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{20}{9}q+\frac{9}{11}b+\frac{20}{11} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a+\frac{14}{9})(\frac{5}{20}-x)& =(\color{red}{a}+\color{orange}{\frac{14}{9}}).(\color{green}{-x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{14}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{4}a-\frac{14}{9}x+\frac{14}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =-ax+\frac{1}{4}a-\frac{14}{9}x+\frac{14}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{1}{4}a-\frac{14}{9}x+\frac{7}{18} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b+\frac{1}{9})(\frac{-13}{6}-x)& =(\color{red}{b}+\color{orange}{\frac{1}{9}}).(\color{green}{-x}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{1}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{6}b-\frac{1}{9}x-\frac{1}{9}.\frac{13}{6}& \text{Uitwerken } \\ & =-bx-\frac{13}{6}b-\frac{1}{9}x-\frac{13}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{1}{19})(x+\frac{-11}{7})& =(\color{red}{a}+\color{orange}{\frac{1}{19}}).(\color{green}{x}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{1}{19})} . \color{green}{(x)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{7}a+\frac{1}{19}x-\frac{1}{19}.\frac{11}{7}& \text{Uitwerken } \\ & =ax-\frac{11}{7}a+\frac{1}{19}x-\frac{11}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-19}{3})(x-\frac{17}{14})& =(\color{red}{b}+\color{orange}{\frac{-19}{3}}).(\color{green}{x}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{14}b-\frac{19}{3}x+\frac{19}{3}.\frac{17}{14}& \text{Uitwerken } \\ & =bx-\frac{17}{14}b-\frac{19}{3}x+\frac{323}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{4}{13})(p-\frac{-9}{17})& =(\color{red}{a}+\color{orange}{\frac{-4}{13}}).(\color{green}{p}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{17}a-\frac{4}{13}p-\frac{4}{13}.\frac{9}{17}& \text{Uitwerken } \\ & =ap+\frac{9}{17}a-\frac{4}{13}p-\frac{36}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-28 23:21:34
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