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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{19}{13}+p)(p+\frac{-13}{20})& =(\color{red}{p}+\color{orange}{\frac{19}{13}}).(\color{green}{p}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{19}{13})} . \color{green}{(p)} + \color{orange}{(\frac{19}{13})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{13}{20}p+\frac{19}{13}p-\frac{19}{13}.\frac{13}{20}& \text{Uitwerken } \\ & =p^2+((\frac{-13}{20})+\frac{19}{13})p-(\frac{-247}{260}) & \text{Neem samen} \\ &=p^2+\frac{211}{260}p-(\frac{-247}{260}) & \text{Maak de som} \\ &=p^2+\frac{211}{260}p+\frac{19}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(p-\frac{14}{10})(x-\frac{-19}{16})& =(\color{red}{p}+\color{orange}{\frac{-7}{5}}).(\color{green}{x}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{19}{16}p-\frac{7}{5}x-\frac{7}{5}.\frac{19}{16}& \text{Uitwerken } \\ & =px+\frac{19}{16}p-\frac{7}{5}x-\frac{133}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{10}{3})(a+\frac{-20}{7})& =(\color{red}{b}+\color{orange}{\frac{10}{3}}).(\color{green}{a}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{20}{7}b+\frac{10}{3}a-\frac{10}{3}.\frac{20}{7}& \text{Uitwerken } \\ & =ab-\frac{20}{7}b+\frac{10}{3}a-\frac{200}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-3}{12}-q)(\frac{1}{20}+b)& =(\color{red}{-q}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{20}q-\frac{1}{4}b-\frac{1}{4}.\frac{1}{20}& \text{Uitwerken } \\ & =-bq-\frac{1}{20}q-\frac{1}{4}b-\frac{1}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{9}-q)(\frac{1}{18}-b)& =(\color{red}{-q}+\color{orange}{\frac{-2}{3}}).(\color{green}{-b}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{18}q+\frac{2}{3}b-\frac{2}{3}.\frac{1}{18}& \text{Uitwerken } \\ & =bq-\frac{1}{18}q+\frac{2}{3}b-\frac{2}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{18}q+\frac{2}{3}b-\frac{1}{27} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-3}{19}+a)(x-\frac{4}{17})& =(\color{red}{a}+\color{orange}{\frac{-3}{19}}).(\color{green}{x}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{-3}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{17}a-\frac{3}{19}x+\frac{3}{19}.\frac{4}{17}& \text{Uitwerken } \\ & =ax-\frac{4}{17}a-\frac{3}{19}x+\frac{12}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-18}{8}+p)(p-\frac{-12}{3})& =(\color{red}{p}+\color{orange}{\frac{-9}{4}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{-9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = pp+4p-\frac{9}{4}p-\frac{9}{4}.4& \text{Uitwerken } \\ & =p^2+(4+(\frac{-9}{4}))p-(\frac{-36}{4}) & \text{Neem samen} \\ &=p^2+\frac{7}{4}p-(\frac{-36}{4}) & \text{Maak de som} \\ &=p^2+\frac{7}{4}p+9 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(\frac{2}{3}-p)(a-\frac{16}{16})& =(\color{red}{-p}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1p+\frac{2}{3}a-\frac{2}{3}.1& \text{Uitwerken } \\ & =-ap+1p+\frac{2}{3}a-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{12}{10})(\frac{3}{18}-p)& =(\color{red}{b}+\color{orange}{\frac{6}{5}}).(\color{green}{-p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{6}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{6}b-\frac{6}{5}p+\frac{6}{5}.\frac{1}{6}& \text{Uitwerken } \\ & =-bp+\frac{1}{6}b-\frac{6}{5}p+\frac{6}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{1}{6}b-\frac{6}{5}p+\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-14}{9})(x+\frac{8}{8})& =(\color{red}{a}+\color{orange}{\frac{-14}{9}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-14}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1a-\frac{14}{9}x-\frac{14}{9}.1& \text{Uitwerken } \\ & =ax+1a-\frac{14}{9}x-\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-15}{3})(\frac{-2}{5}-q)& =(\color{red}{a}+\color{orange}{5}).(\color{green}{-q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(5)} . \color{green}{(-q)} + \color{orange}{(5)} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{2}{5}a-5q-5.\frac{2}{5}& \text{Uitwerken } \\ & =-aq-\frac{2}{5}a-5q-\frac{10}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{2}{5}a-5q-2 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-7}{10}+q)(b-\frac{-16}{11})& =(\color{red}{q}+\color{orange}{\frac{-7}{10}}).(\color{green}{b}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{16}{11}q-\frac{7}{10}b-\frac{7}{10}.\frac{16}{11}& \text{Uitwerken } \\ & =bq+\frac{16}{11}q-\frac{7}{10}b-\frac{112}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{16}{11}q-\frac{7}{10}b-\frac{56}{55} & \text{Vereenvoudig} \\\end{align}\)
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