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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-4}{2})(x+\frac{17}{11})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{11}b-2x-2.\frac{17}{11}& \text{Uitwerken } \\ & =bx+\frac{17}{11}b-2x-\frac{34}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{5}{10}+b)(\frac{-4}{12}+q)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{3}b+\frac{1}{2}q-\frac{1}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =bq-\frac{1}{3}b+\frac{1}{2}q-\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-8}{17}+p)(\frac{-17}{13}+p)& =(\color{red}{p}+\color{orange}{\frac{-8}{17}}).(\color{green}{p}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{13}p-\frac{8}{17}p+\frac{8}{17}.\frac{17}{13}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{13})+(\frac{-8}{17}))p+\frac{136}{221} & \text{Neem samen} \\ &=p^2-\frac{393}{221}p+\frac{136}{221} & \text{Maak de som} \\ &=p^2-\frac{393}{221}p+\frac{8}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-13}{4})(\frac{-3}{2}-b)& =(\color{red}{q}+\color{orange}{\frac{13}{4}}).(\color{green}{-b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{13}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{2}q-\frac{13}{4}b-\frac{13}{4}.\frac{3}{2}& \text{Uitwerken } \\ & =-bq-\frac{3}{2}q-\frac{13}{4}b-\frac{39}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-7}{6}+a)(p-\frac{-8}{16})& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{2}a-\frac{7}{6}p-\frac{7}{6}.\frac{1}{2}& \text{Uitwerken } \\ & =ap+\frac{1}{2}a-\frac{7}{6}p-\frac{7}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-15}{11})(q+\frac{-9}{19})& =(\color{red}{x}+\color{orange}{\frac{-15}{11}}).(\color{green}{q}+\color{blue}{\frac{-9}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{19})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-9}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{19}x-\frac{15}{11}q+\frac{15}{11}.\frac{9}{19}& \text{Uitwerken } \\ & =qx-\frac{9}{19}x-\frac{15}{11}q+\frac{135}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-2}{20}+p)(q+\frac{-11}{11})& =(\color{red}{p}+\color{orange}{\frac{-1}{10}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1p-\frac{1}{10}q+\frac{1}{10}.1& \text{Uitwerken } \\ & =pq-1p-\frac{1}{10}q+\frac{1}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-17}{16})(\frac{-16}{19}-q)& =(\color{red}{q}+\color{orange}{\frac{-17}{16}}).(\color{green}{-q}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{16}{19}q+\frac{17}{16}q+\frac{17}{16}.\frac{16}{19}& \text{Uitwerken } \\ & =-q^2+((\frac{-16}{19})+\frac{17}{16})q+(\frac{-272}{304}) & \text{Neem samen} \\ &=-q^2+\frac{67}{304}q+(\frac{-272}{304}) & \text{Maak de som} \\ &=-q^2+\frac{67}{304}q+(\frac{-17}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{19}{17}+b)(p+\frac{11}{20})& =(\color{red}{b}+\color{orange}{\frac{19}{17}}).(\color{green}{p}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{19}{17})} . \color{green}{(p)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{20}b+\frac{19}{17}p+\frac{19}{17}.\frac{11}{20}& \text{Uitwerken } \\ & =bp+\frac{11}{20}b+\frac{19}{17}p+\frac{209}{340} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-20}{15})(p+\frac{5}{15})& =(\color{red}{a}+\color{orange}{\frac{4}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{3}a+\frac{4}{3}p+\frac{4}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =ap+\frac{1}{3}a+\frac{4}{3}p+\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{11}-q)(b-\frac{1}{16})& =(\color{red}{-q}+\color{orange}{\frac{-14}{11}}).(\color{green}{b}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{16}q-\frac{14}{11}b+\frac{14}{11}.\frac{1}{16}& \text{Uitwerken } \\ & =-bq+\frac{1}{16}q-\frac{14}{11}b+\frac{14}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{1}{16}q-\frac{14}{11}b+\frac{7}{88} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-7}{14})(p-(-13))& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{13})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(13)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = pq+13q-\frac{1}{2}p-\frac{1}{2}.13& \text{Uitwerken } \\ & =pq+13q-\frac{1}{2}p-\frac{13}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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