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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{13}{17}+a)(\frac{18}{11}-a)& =(\color{red}{a}+\color{orange}{\frac{13}{17}}).(\color{green}{-a}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(\frac{13}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{18}{11}a-\frac{13}{17}a+\frac{13}{17}.\frac{18}{11}& \text{Uitwerken } \\ & =-a^2+(\frac{18}{11}+(\frac{-13}{17}))a+(\frac{-234}{187}) & \text{Neem samen} \\ &=-a^2+\frac{163}{187}a+(\frac{-234}{187}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-13}{13})(\frac{-13}{11}+p)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{11}q+1p-1.\frac{13}{11}& \text{Uitwerken } \\ & =pq-\frac{13}{11}q+1p-\frac{13}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{18}{20})(q+\frac{-4}{20})& =(\color{red}{a}+\color{orange}{\frac{-9}{10}}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{5}a-\frac{9}{10}q+\frac{9}{10}.\frac{1}{5}& \text{Uitwerken } \\ & =aq-\frac{1}{5}a-\frac{9}{10}q+\frac{9}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{5}-q)(\frac{-1}{19}-b)& =(\color{red}{-q}+\color{orange}{\frac{11}{5}}).(\color{green}{-b}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{11}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{19}q-\frac{11}{5}b-\frac{11}{5}.\frac{1}{19}& \text{Uitwerken } \\ & =bq+\frac{1}{19}q-\frac{11}{5}b-\frac{11}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+2)(\frac{1}{5}-x)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{-x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(2)} . \color{green}{(-x)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{5}q-2x+2.\frac{1}{5}& \text{Uitwerken } \\ & =-qx+\frac{1}{5}q-2x+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{9}{14})(b+\frac{18}{5})& =(\color{red}{q}+\color{orange}{\frac{9}{14}}).(\color{green}{b}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{9}{14})} . \color{green}{(b)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{5}q+\frac{9}{14}b+\frac{9}{14}.\frac{18}{5}& \text{Uitwerken } \\ & =bq+\frac{18}{5}q+\frac{9}{14}b+\frac{162}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{18}{5}q+\frac{9}{14}b+\frac{81}{35} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{16}{13})(b-\frac{-16}{6})& =(\color{red}{x}+\color{orange}{\frac{-16}{13}}).(\color{green}{b}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{8}{3}x-\frac{16}{13}b-\frac{16}{13}.\frac{8}{3}& \text{Uitwerken } \\ & =bx+\frac{8}{3}x-\frac{16}{13}b-\frac{128}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{19}{17})(p+\frac{-12}{8})& =(\color{red}{a}+\color{orange}{\frac{19}{17}}).(\color{green}{p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{19}{17})} . \color{green}{(p)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{2}a+\frac{19}{17}p-\frac{19}{17}.\frac{3}{2}& \text{Uitwerken } \\ & =ap-\frac{3}{2}a+\frac{19}{17}p-\frac{57}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{2}{2})(\frac{-14}{3}+x)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{14}{3}q+1x-1.\frac{14}{3}& \text{Uitwerken } \\ & =qx-\frac{14}{3}q+1x-\frac{14}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{11}{20})(\frac{-16}{20}-p)& =(\color{red}{p}+\color{orange}{\frac{11}{20}}).(\color{green}{-p}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{11}{20})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{4}{5}p-\frac{11}{20}p-\frac{11}{20}.\frac{4}{5}& \text{Uitwerken } \\ & =-p^2+((\frac{-4}{5})+(\frac{-11}{20}))p-\frac{44}{100} & \text{Neem samen} \\ &=-p^2-\frac{27}{20}p-\frac{44}{100} & \text{Maak de som} \\ &=-p^2-\frac{27}{20}p-\frac{11}{25} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}((-16)+x)(p-\frac{19}{10})& =(\color{red}{x}+\color{orange}{(-16)}).(\color{green}{p}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(-16)} . \color{green}{(p)} + \color{orange}{(-16)} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{10}x-16p+16.\frac{19}{10}& \text{Uitwerken } \\ & =px-\frac{19}{10}x-16p+\frac{304}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{19}{10}x-16p+\frac{152}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-4}{6}+x)(\frac{-17}{17}+p)& =(\color{red}{x}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1x-\frac{2}{3}p+\frac{2}{3}.1& \text{Uitwerken } \\ & =px-1x-\frac{2}{3}p+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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