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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{4}{13})(x-\frac{-20}{3})& =(\color{red}{a}+\color{orange}{\frac{4}{13}}).(\color{green}{x}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{4}{13})} . \color{green}{(x)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{20}{3}a+\frac{4}{13}x+\frac{4}{13}.\frac{20}{3}& \text{Uitwerken } \\ & =ax+\frac{20}{3}a+\frac{4}{13}x+\frac{80}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{13}{3})(\frac{3}{2}-x)& =(\color{red}{b}+\color{orange}{\frac{-13}{3}}).(\color{green}{-x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-13}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{2}b+\frac{13}{3}x-\frac{13}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =-bx+\frac{3}{2}b+\frac{13}{3}x-\frac{39}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{3}{2}b+\frac{13}{3}x-\frac{13}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{19}{9}-p)(\frac{-3}{2}-x)& =(\color{red}{-p}+\color{orange}{\frac{19}{9}}).(\color{green}{-x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{19}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{2}p-\frac{19}{9}x-\frac{19}{9}.\frac{3}{2}& \text{Uitwerken } \\ & =px+\frac{3}{2}p-\frac{19}{9}x-\frac{57}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{3}{2}p-\frac{19}{9}x-\frac{19}{6} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-4}{5})(a+\frac{16}{7})& =(\color{red}{a}+\color{orange}{\frac{-4}{5}}).(\color{green}{a}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{16}{7}a-\frac{4}{5}a-\frac{4}{5}.\frac{16}{7}& \text{Uitwerken } \\ & =a^2+(\frac{16}{7}+(\frac{-4}{5}))a-(\frac{-64}{35}) & \text{Neem samen} \\ &=a^2+\frac{52}{35}a-(\frac{-64}{35}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(b+\frac{-9}{5})(q+\frac{-6}{20})& =(\color{red}{b}+\color{orange}{\frac{-9}{5}}).(\color{green}{q}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{10}b-\frac{9}{5}q+\frac{9}{5}.\frac{3}{10}& \text{Uitwerken } \\ & =bq-\frac{3}{10}b-\frac{9}{5}q+\frac{27}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-17}{4})(\frac{5}{14}+x)& =(\color{red}{q}+\color{orange}{\frac{17}{4}}).(\color{green}{x}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{17}{4})} . \color{green}{(x)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{14}q+\frac{17}{4}x+\frac{17}{4}.\frac{5}{14}& \text{Uitwerken } \\ & =qx+\frac{5}{14}q+\frac{17}{4}x+\frac{85}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{6}{3}-b)(\frac{-8}{17}+x)& =(\color{red}{-b}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{8}{17}b+2x-2.\frac{8}{17}& \text{Uitwerken } \\ & =-bx+\frac{8}{17}b+2x-\frac{16}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{5}{20})(\frac{13}{7}+b)& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{7}a-\frac{1}{4}b-\frac{1}{4}.\frac{13}{7}& \text{Uitwerken } \\ & =ab+\frac{13}{7}a-\frac{1}{4}b-\frac{13}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-13}{10})(\frac{-16}{12}+q)& =(\color{red}{p}+\color{orange}{\frac{13}{10}}).(\color{green}{q}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{3}p+\frac{13}{10}q-\frac{13}{10}.\frac{4}{3}& \text{Uitwerken } \\ & =pq-\frac{4}{3}p+\frac{13}{10}q-\frac{52}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{4}{3}p+\frac{13}{10}q-\frac{26}{15} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{16}{7}+b)(\frac{-2}{9}-q)& =(\color{red}{b}+\color{orange}{\frac{16}{7}}).(\color{green}{-q}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{16}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{2}{9}b-\frac{16}{7}q-\frac{16}{7}.\frac{2}{9}& \text{Uitwerken } \\ & =-bq-\frac{2}{9}b-\frac{16}{7}q-\frac{32}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-20}{3})(b-\frac{18}{7})& =(\color{red}{a}+\color{orange}{\frac{20}{3}}).(\color{green}{b}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{20}{3})} . \color{green}{(b)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{18}{7}a+\frac{20}{3}b-\frac{20}{3}.\frac{18}{7}& \text{Uitwerken } \\ & =ab-\frac{18}{7}a+\frac{20}{3}b-\frac{360}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{18}{7}a+\frac{20}{3}b-\frac{120}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-1}{15}+x)(\frac{1}{17}+q)& =(\color{red}{x}+\color{orange}{\frac{-1}{15}}).(\color{green}{q}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{17}x-\frac{1}{15}q-\frac{1}{15}.\frac{1}{17}& \text{Uitwerken } \\ & =qx+\frac{1}{17}x-\frac{1}{15}q-\frac{1}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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