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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{6}{6})(\frac{5}{19}-q)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{\frac{5}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{19})} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{19}b+1q-1.\frac{5}{19}& \text{Uitwerken } \\ & =-bq+\frac{5}{19}b+1q-\frac{5}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-2}{17})(\frac{-9}{4}-a)& =(\color{red}{q}+\color{orange}{\frac{2}{17}}).(\color{green}{-a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{2}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{9}{4}q-\frac{2}{17}a-\frac{2}{17}.\frac{9}{4}& \text{Uitwerken } \\ & =-aq-\frac{9}{4}q-\frac{2}{17}a-\frac{18}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{9}{4}q-\frac{2}{17}a-\frac{9}{34} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{16}{6}-a)(\frac{-3}{2}+x)& =(\color{red}{-a}+\color{orange}{\frac{8}{3}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{2}a+\frac{8}{3}x-\frac{8}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =-ax+\frac{3}{2}a+\frac{8}{3}x-\frac{24}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{3}{2}a+\frac{8}{3}x-4 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{20}+p)(\frac{3}{7}-a)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{7}p-1a+1.\frac{3}{7}& \text{Uitwerken } \\ & =-ap+\frac{3}{7}p-1a+\frac{3}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{13}{6})(\frac{5}{6}+q)& =(\color{red}{a}+\color{orange}{\frac{13}{6}}).(\color{green}{q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{13}{6})} . \color{green}{(q)} + \color{orange}{(\frac{13}{6})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{6}a+\frac{13}{6}q+\frac{13}{6}.\frac{5}{6}& \text{Uitwerken } \\ & =aq+\frac{5}{6}a+\frac{13}{6}q+\frac{65}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-19}{20}+q)(q-\frac{-6}{14})& =(\color{red}{q}+\color{orange}{\frac{-19}{20}}).(\color{green}{q}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{7}q-\frac{19}{20}q-\frac{19}{20}.\frac{3}{7}& \text{Uitwerken } \\ & =q^2+(\frac{3}{7}+(\frac{-19}{20}))q-(\frac{-57}{140}) & \text{Neem samen} \\ &=q^2-\frac{73}{140}q-(\frac{-57}{140}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-8}{7})(\frac{12}{18}-a)& =(\color{red}{b}+\color{orange}{\frac{8}{7}}).(\color{green}{-a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{8}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{2}{3}b-\frac{8}{7}a+\frac{8}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =-ab+\frac{2}{3}b-\frac{8}{7}a+\frac{16}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{15}+a)(\frac{12}{16}+a)& =(\color{red}{a}+\color{orange}{\frac{-1}{5}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{4}a-\frac{1}{5}a-\frac{1}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =a^2+(\frac{3}{4}+(\frac{-1}{5}))a-(\frac{-3}{20}) & \text{Neem samen} \\ &=a^2+\frac{11}{20}a-(\frac{-3}{20}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(a+16)(\frac{2}{4}-a)& =(\color{red}{a}+\color{orange}{16}).(\color{green}{-a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(16)} . \color{green}{(-a)} + \color{orange}{(16)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{2}a-16a+16.\frac{1}{2}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{2}+(-16))a+(\frac{-16}{2}) & \text{Neem samen} \\ &=-a^2-\frac{31}{2}a+(\frac{-16}{2}) & \text{Maak de som} \\ &=-a^2-\frac{31}{2}a+(-8) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{8}{10}+p)(\frac{-10}{16}+q)& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{q}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{8}p+\frac{4}{5}q-\frac{4}{5}.\frac{5}{8}& \text{Uitwerken } \\ & =pq-\frac{5}{8}p+\frac{4}{5}q-\frac{20}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{5}{8}p+\frac{4}{5}q-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{18}{4}-x)(q+\frac{19}{9})& =(\color{red}{-x}+\color{orange}{\frac{9}{2}}).(\color{green}{q}+\color{blue}{\frac{19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{9})} + \color{orange}{(\frac{9}{2})} . \color{green}{(q)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{19}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{9}x+\frac{9}{2}q+\frac{9}{2}.\frac{19}{9}& \text{Uitwerken } \\ & =-qx-\frac{19}{9}x+\frac{9}{2}q+\frac{171}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{19}{9}x+\frac{9}{2}q+\frac{19}{2} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-3}{7})(\frac{-14}{18}-p)& =(\color{red}{a}+\color{orange}{\frac{3}{7}}).(\color{green}{-p}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{3}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{7}{9}a-\frac{3}{7}p-\frac{3}{7}.\frac{7}{9}& \text{Uitwerken } \\ & =-ap-\frac{7}{9}a-\frac{3}{7}p-\frac{21}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{7}{9}a-\frac{3}{7}p-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
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