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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{1}{17}-a)(q+\frac{-5}{17})& =(\color{red}{-a}+\color{orange}{\frac{1}{17}}).(\color{green}{q}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{1}{17})} . \color{green}{(q)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{17}a+\frac{1}{17}q-\frac{1}{17}.\frac{5}{17}& \text{Uitwerken } \\ & =-aq+\frac{5}{17}a+\frac{1}{17}q-\frac{5}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{7}{7}-a)(\frac{16}{2}-p)& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{8})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(8)} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = ap-8a-1p+1.8& \text{Uitwerken } \\ & =ap-8a-1p+8 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{18}{15})(\frac{-5}{14}+p)& =(\color{red}{b}+\color{orange}{\frac{6}{5}}).(\color{green}{p}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{6}{5})} . \color{green}{(p)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{14}b+\frac{6}{5}p-\frac{6}{5}.\frac{5}{14}& \text{Uitwerken } \\ & =bp-\frac{5}{14}b+\frac{6}{5}p-\frac{30}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{5}{14}b+\frac{6}{5}p-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-11}{18})(\frac{-4}{5}-a)& =(\color{red}{a}+\color{orange}{\frac{-11}{18}}).(\color{green}{-a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{4}{5}a+\frac{11}{18}a+\frac{11}{18}.\frac{4}{5}& \text{Uitwerken } \\ & =-a^2+((\frac{-4}{5})+\frac{11}{18})a+(\frac{-44}{90}) & \text{Neem samen} \\ &=-a^2-\frac{17}{90}a+(\frac{-44}{90}) & \text{Maak de som} \\ &=-a^2-\frac{17}{90}a+(\frac{-22}{45}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-11}{12}+p)(\frac{-9}{5}-b)& =(\color{red}{p}+\color{orange}{\frac{-11}{12}}).(\color{green}{-b}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{9}{5}p+\frac{11}{12}b+\frac{11}{12}.\frac{9}{5}& \text{Uitwerken } \\ & =-bp-\frac{9}{5}p+\frac{11}{12}b+\frac{99}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{9}{5}p+\frac{11}{12}b+\frac{33}{20} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{7}{2})(\frac{1}{5}-b)& =(\color{red}{b}+\color{orange}{\frac{-7}{2}}).(\color{green}{-b}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{5}b+\frac{7}{2}b-\frac{7}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{5}+\frac{7}{2})b-\frac{7}{10} & \text{Neem samen} \\ &=-b^2+\frac{37}{10}b-\frac{7}{10} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-4}{16}+x)(\frac{7}{3}-x)& =(\color{red}{x}+\color{orange}{\frac{-1}{4}}).(\color{green}{-x}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{7}{3}x+\frac{1}{4}x-\frac{1}{4}.\frac{7}{3}& \text{Uitwerken } \\ & =-x^2+(\frac{7}{3}+\frac{1}{4})x-\frac{7}{12} & \text{Neem samen} \\ &=-x^2+\frac{31}{12}x-\frac{7}{12} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-11}{13})(\frac{18}{8}-x)& =(\color{red}{a}+\color{orange}{\frac{11}{13}}).(\color{green}{-x}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{11}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{4}a-\frac{11}{13}x+\frac{11}{13}.\frac{9}{4}& \text{Uitwerken } \\ & =-ax+\frac{9}{4}a-\frac{11}{13}x+\frac{99}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{18}{14}+p)(\frac{19}{12}-a)& =(\color{red}{p}+\color{orange}{\frac{9}{7}}).(\color{green}{-a}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{9}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{12}p-\frac{9}{7}a+\frac{9}{7}.\frac{19}{12}& \text{Uitwerken } \\ & =-ap+\frac{19}{12}p-\frac{9}{7}a+\frac{171}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{19}{12}p-\frac{9}{7}a+\frac{57}{28} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-11}{19})(a-\frac{13}{6})& =(\color{red}{x}+\color{orange}{\frac{11}{19}}).(\color{green}{a}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{11}{19})} . \color{green}{(a)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{6}x+\frac{11}{19}a-\frac{11}{19}.\frac{13}{6}& \text{Uitwerken } \\ & =ax-\frac{13}{6}x+\frac{11}{19}a-\frac{143}{114} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-(-13))(\frac{14}{15}-q)& =(\color{red}{p}+\color{orange}{13}).(\color{green}{-q}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(13)} . \color{green}{(-q)} + \color{orange}{(13)} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{14}{15}p-13q+13.\frac{14}{15}& \text{Uitwerken } \\ & =-pq+\frac{14}{15}p-13q+\frac{182}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x-\frac{14}{3})(\frac{17}{8}-a)& =(\color{red}{x}+\color{orange}{\frac{-14}{3}}).(\color{green}{-a}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{17}{8}x+\frac{14}{3}a-\frac{14}{3}.\frac{17}{8}& \text{Uitwerken } \\ & =-ax+\frac{17}{8}x+\frac{14}{3}a-\frac{238}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{17}{8}x+\frac{14}{3}a-\frac{119}{12} & \text{Vereenvoudig} \\\end{align}\)
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