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

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

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Verbetersleutel

  1. \(\begin{align}(a+\frac{-18}{16})(b+\frac{-2}{17})& =(\color{red}{a}+\color{orange}{\frac{-9}{8}}).(\color{green}{b}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{17}a-\frac{9}{8}b+\frac{9}{8}.\frac{2}{17}& \text{Uitwerken } \\ & =ab-\frac{2}{17}a-\frac{9}{8}b+\frac{18}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{2}{17}a-\frac{9}{8}b+\frac{9}{68} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x+\frac{-20}{5})(a-\frac{20}{12})& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{3}x-4a+4.\frac{5}{3}& \text{Uitwerken } \\ & =ax-\frac{5}{3}x-4a+\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{11}{6}+b)((-18)-q)& =(\color{red}{b}+\color{orange}{\frac{11}{6}}).(\color{green}{-q}+\color{blue}{(-18)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(-18)} + \color{orange}{(\frac{11}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = -bq-18b-\frac{11}{6}q-\frac{11}{6}.18& \text{Uitwerken } \\ & =-bq-18b-\frac{11}{6}q-\frac{198}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-18b-\frac{11}{6}q-33 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{14}{10}-q)(x-\frac{-6}{9})& =(\color{red}{-q}+\color{orange}{\frac{7}{5}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{3}q+\frac{7}{5}x+\frac{7}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =-qx-\frac{2}{3}q+\frac{7}{5}x+\frac{14}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-7}{2}-x)(x-\frac{15}{9})& =(\color{red}{-x}+\color{orange}{\frac{-7}{2}}).(\color{green}{x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{5}{3}x-\frac{7}{2}x+\frac{7}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =-x^2+(\frac{5}{3}+(\frac{-7}{2}))x+(\frac{-35}{6}) & \text{Neem samen} \\ &=-x^2-\frac{11}{6}x+(\frac{-35}{6}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(a+\frac{16}{7})(\frac{-18}{16}+a)& =(\color{red}{a}+\color{orange}{\frac{16}{7}}).(\color{green}{a}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{16}{7})} . \color{green}{(a)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{9}{8}a+\frac{16}{7}a-\frac{16}{7}.\frac{9}{8}& \text{Uitwerken } \\ & =a^2+((\frac{-9}{8})+\frac{16}{7})a-(\frac{-144}{56}) & \text{Neem samen} \\ &=a^2+\frac{65}{56}a-(\frac{-144}{56}) & \text{Maak de som} \\ &=a^2+\frac{65}{56}a+\frac{18}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(b+\frac{4}{3})(\frac{19}{13}+q)& =(\color{red}{b}+\color{orange}{\frac{4}{3}}).(\color{green}{q}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(\frac{4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{13}b+\frac{4}{3}q+\frac{4}{3}.\frac{19}{13}& \text{Uitwerken } \\ & =bq+\frac{19}{13}b+\frac{4}{3}q+\frac{76}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-19}{5})(\frac{-3}{5}-x)& =(\color{red}{q}+\color{orange}{\frac{19}{5}}).(\color{green}{-x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{19}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{5})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{5}q-\frac{19}{5}x-\frac{19}{5}.\frac{3}{5}& \text{Uitwerken } \\ & =-qx-\frac{3}{5}q-\frac{19}{5}x-\frac{57}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{16}{6}+x)(p+\frac{-11}{6})& =(\color{red}{x}+\color{orange}{\frac{8}{3}}).(\color{green}{p}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{6}x+\frac{8}{3}p-\frac{8}{3}.\frac{11}{6}& \text{Uitwerken } \\ & =px-\frac{11}{6}x+\frac{8}{3}p-\frac{88}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{11}{6}x+\frac{8}{3}p-\frac{44}{9} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-1}{5}+x)(\frac{-19}{15}-x)& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{-x}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{19}{15}x+\frac{1}{5}x+\frac{1}{5}.\frac{19}{15}& \text{Uitwerken } \\ & =-x^2+((\frac{-19}{15})+\frac{1}{5})x+(\frac{-19}{75}) & \text{Neem samen} \\ &=-x^2-\frac{16}{15}x+(\frac{-19}{75}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a-\frac{19}{2})(\frac{-6}{10}+b)& =(\color{red}{a}+\color{orange}{\frac{-19}{2}}).(\color{green}{b}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{5}a-\frac{19}{2}b+\frac{19}{2}.\frac{3}{5}& \text{Uitwerken } \\ & =ab-\frac{3}{5}a-\frac{19}{2}b+\frac{57}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{16}+a)((-8)+b)& =(\color{red}{a}+\color{orange}{\frac{-1}{8}}).(\color{green}{b}+\color{blue}{(-8)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-8)} + \color{orange}{(\frac{-1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = ab-8a-\frac{1}{8}b+\frac{1}{8}.8& \text{Uitwerken } \\ & =ab-8a-\frac{1}{8}b+\frac{8}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-8a-\frac{1}{8}b+1 & \text{Vereenvoudig} \\\end{align}\)
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