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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{15}{5})(\frac{-12}{3}+p)& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = pq-4q-3p+3.4& \text{Uitwerken } \\ & =pq-4q-3p+12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-20}{8})(\frac{4}{9}-q)& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{-q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{4}{9}b+\frac{5}{2}q-\frac{5}{2}.\frac{4}{9}& \text{Uitwerken } \\ & =-bq+\frac{4}{9}b+\frac{5}{2}q-\frac{20}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{4}{9}b+\frac{5}{2}q-\frac{10}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{3}{5}+q)(a+\frac{11}{11})& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aq+1q+\frac{3}{5}a+\frac{3}{5}.1& \text{Uitwerken } \\ & =aq+1q+\frac{3}{5}a+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{1}{7})(q-\frac{-18}{8})& =(\color{red}{q}+\color{orange}{\frac{-1}{7}}).(\color{green}{q}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{9}{4}q-\frac{1}{7}q-\frac{1}{7}.\frac{9}{4}& \text{Uitwerken } \\ & =q^2+(\frac{9}{4}+(\frac{-1}{7}))q-(\frac{-9}{28}) & \text{Neem samen} \\ &=q^2+\frac{59}{28}q-(\frac{-9}{28}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a+\frac{19}{7})(\frac{1}{9}-q)& =(\color{red}{a}+\color{orange}{\frac{19}{7}}).(\color{green}{-q}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{19}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{9}a-\frac{19}{7}q+\frac{19}{7}.\frac{1}{9}& \text{Uitwerken } \\ & =-aq+\frac{1}{9}a-\frac{19}{7}q+\frac{19}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-4}{15}-b)(\frac{-6}{10}+q)& =(\color{red}{-b}+\color{orange}{\frac{-4}{15}}).(\color{green}{q}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{5}b-\frac{4}{15}q+\frac{4}{15}.\frac{3}{5}& \text{Uitwerken } \\ & =-bq+\frac{3}{5}b-\frac{4}{15}q+\frac{12}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{3}{5}b-\frac{4}{15}q+\frac{4}{25} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{17}-x)(\frac{7}{17}-p)& =(\color{red}{-x}+\color{orange}{\frac{-14}{17}}).(\color{green}{-p}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{17}x+\frac{14}{17}p-\frac{14}{17}.\frac{7}{17}& \text{Uitwerken } \\ & =px-\frac{7}{17}x+\frac{14}{17}p-\frac{98}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-11}{14}+x)(\frac{15}{15}-b)& =(\color{red}{x}+\color{orange}{\frac{-11}{14}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-11}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1x+\frac{11}{14}b-\frac{11}{14}.1& \text{Uitwerken } \\ & =-bx+1x+\frac{11}{14}b-\frac{11}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{14}{14})(p+\frac{11}{3})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{11}{3}p-1p-1.\frac{11}{3}& \text{Uitwerken } \\ & =p^2+(\frac{11}{3}+(-1))p-(\frac{-11}{3}) & \text{Neem samen} \\ &=p^2+\frac{8}{3}p-(\frac{-11}{3}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-18}{12}+a)(\frac{-1}{15}-x)& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{-x}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{15}a+\frac{3}{2}x+\frac{3}{2}.\frac{1}{15}& \text{Uitwerken } \\ & =-ax-\frac{1}{15}a+\frac{3}{2}x+\frac{3}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{1}{15}a+\frac{3}{2}x+\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-15}{14}+q)(\frac{5}{17}+a)& =(\color{red}{q}+\color{orange}{\frac{-15}{14}}).(\color{green}{a}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{17}q-\frac{15}{14}a-\frac{15}{14}.\frac{5}{17}& \text{Uitwerken } \\ & =aq+\frac{5}{17}q-\frac{15}{14}a-\frac{75}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{2}{20})(\frac{20}{2}-a)& =(\color{red}{a}+\color{orange}{\frac{-1}{10}}).(\color{green}{-a}+\color{blue}{10})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(10)} + \color{orange}{(\frac{-1}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -aa+10a+\frac{1}{10}a-\frac{1}{10}.10& \text{Uitwerken } \\ & =-a^2+(10+\frac{1}{10})a-\frac{10}{10} & \text{Neem samen} \\ &=-a^2+\frac{101}{10}a-\frac{10}{10} & \text{Maak de som} \\ &=-a^2+\frac{101}{10}a-1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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