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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{19}{7})(\frac{-3}{17}-q)& =(\color{red}{b}+\color{orange}{\frac{-19}{7}}).(\color{green}{-q}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{17}b+\frac{19}{7}q+\frac{19}{7}.\frac{3}{17}& \text{Uitwerken } \\ & =-bq-\frac{3}{17}b+\frac{19}{7}q+\frac{57}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{9}+x)(\frac{-16}{10}-p)& =(\color{red}{x}+\color{orange}{\frac{-4}{3}}).(\color{green}{-p}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{8}{5}x+\frac{4}{3}p+\frac{4}{3}.\frac{8}{5}& \text{Uitwerken } \\ & =-px-\frac{8}{5}x+\frac{4}{3}p+\frac{32}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{12}{2}+p)(\frac{2}{11}+p)& =(\color{red}{p}+\color{orange}{6}).(\color{green}{p}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(6)} . \color{green}{(p)} + \color{orange}{(6)} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{2}{11}p+6p+6.\frac{2}{11}& \text{Uitwerken } \\ & =p^2+(\frac{2}{11}+6)p+\frac{12}{11} & \text{Neem samen} \\ &=p^2+\frac{68}{11}p+\frac{12}{11} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-20}{11}+p)(x-\frac{11}{19})& =(\color{red}{p}+\color{orange}{\frac{-20}{11}}).(\color{green}{x}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{19}p-\frac{20}{11}x+\frac{20}{11}.\frac{11}{19}& \text{Uitwerken } \\ & =px-\frac{11}{19}p-\frac{20}{11}x+\frac{220}{209} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{11}{19}p-\frac{20}{11}x+\frac{20}{19} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{10}-p)(\frac{20}{5}+b)& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(4)} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -bp-4p+1b+1.4& \text{Uitwerken } \\ & =-bp-4p+1b+4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{16}{9}+p)(\frac{13}{20}-q)& =(\color{red}{p}+\color{orange}{\frac{16}{9}}).(\color{green}{-q}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{16}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{13}{20}p-\frac{16}{9}q+\frac{16}{9}.\frac{13}{20}& \text{Uitwerken } \\ & =-pq+\frac{13}{20}p-\frac{16}{9}q+\frac{208}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{13}{20}p-\frac{16}{9}q+\frac{52}{45} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{3}-p)(\frac{19}{19}+b)& =(\color{red}{-p}+\color{orange}{\frac{13}{3}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{13}{3})} . \color{green}{(b)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1p+\frac{13}{3}b+\frac{13}{3}.1& \text{Uitwerken } \\ & =-bp-1p+\frac{13}{3}b+\frac{13}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(18+b)(\frac{-5}{6}+q)& =(\color{red}{b}+\color{orange}{18}).(\color{green}{q}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(18)} . \color{green}{(q)} + \color{orange}{(18)} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{6}b+18q-18.\frac{5}{6}& \text{Uitwerken } \\ & =bq-\frac{5}{6}b+18q-\frac{90}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{5}{6}b+18q-15 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-4}{20}+x)(\frac{13}{13}-a)& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ax+1x+\frac{1}{5}a-\frac{1}{5}.1& \text{Uitwerken } \\ & =-ax+1x+\frac{1}{5}a-\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{9}{6}+b)(a+\frac{-6}{13})& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{6}{13}b+\frac{3}{2}a-\frac{3}{2}.\frac{6}{13}& \text{Uitwerken } \\ & =ab-\frac{6}{13}b+\frac{3}{2}a-\frac{18}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{6}{13}b+\frac{3}{2}a-\frac{9}{13} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-16}{5}-a)(x-\frac{8}{2})& =(\color{red}{-a}+\color{orange}{\frac{-16}{5}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-16}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ax+4a-\frac{16}{5}x+\frac{16}{5}.4& \text{Uitwerken } \\ & =-ax+4a-\frac{16}{5}x+\frac{64}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{4}{19}-a)(p-\frac{-17}{20})& =(\color{red}{-a}+\color{orange}{\frac{4}{19}}).(\color{green}{p}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{4}{19})} . \color{green}{(p)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{20}a+\frac{4}{19}p+\frac{4}{19}.\frac{17}{20}& \text{Uitwerken } \\ & =-ap-\frac{17}{20}a+\frac{4}{19}p+\frac{68}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{17}{20}a+\frac{4}{19}p+\frac{17}{95} & \text{Vereenvoudig} \\\end{align}\)
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