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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-17}{18}+a)(\frac{-11}{3}+a)& =(\color{red}{a}+\color{orange}{\frac{-17}{18}}).(\color{green}{a}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{11}{3}a-\frac{17}{18}a+\frac{17}{18}.\frac{11}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-11}{3})+(\frac{-17}{18}))a+\frac{187}{54} & \text{Neem samen} \\ &=a^2-\frac{83}{18}a+\frac{187}{54} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-19}{8}+b)(\frac{-11}{10}-x)& =(\color{red}{b}+\color{orange}{\frac{-19}{8}}).(\color{green}{-x}+\color{blue}{\frac{-11}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{10})} + \color{orange}{(\frac{-19}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(\frac{-11}{10})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{11}{10}b+\frac{19}{8}x+\frac{19}{8}.\frac{11}{10}& \text{Uitwerken } \\ & =-bx-\frac{11}{10}b+\frac{19}{8}x+\frac{209}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-4}{19})(\frac{14}{11}+x)& =(\color{red}{q}+\color{orange}{\frac{-4}{19}}).(\color{green}{x}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{-4}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{19})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{14}{11}q-\frac{4}{19}x-\frac{4}{19}.\frac{14}{11}& \text{Uitwerken } \\ & =qx+\frac{14}{11}q-\frac{4}{19}x-\frac{56}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{1}{17})(p-\frac{-3}{7})& =(\color{red}{q}+\color{orange}{\frac{1}{17}}).(\color{green}{p}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{1}{17})} . \color{green}{(p)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{7}q+\frac{1}{17}p+\frac{1}{17}.\frac{3}{7}& \text{Uitwerken } \\ & =pq+\frac{3}{7}q+\frac{1}{17}p+\frac{3}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-18}{11}+a)(x+\frac{-9}{18})& =(\color{red}{a}+\color{orange}{\frac{-18}{11}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-18}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{11})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{2}a-\frac{18}{11}x+\frac{18}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =ax-\frac{1}{2}a-\frac{18}{11}x+\frac{18}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{1}{2}a-\frac{18}{11}x+\frac{9}{11} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-13}{9})(\frac{9}{6}+a)& =(\color{red}{x}+\color{orange}{\frac{-13}{9}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{2}x-\frac{13}{9}a-\frac{13}{9}.\frac{3}{2}& \text{Uitwerken } \\ & =ax+\frac{3}{2}x-\frac{13}{9}a-\frac{39}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{2}x-\frac{13}{9}a-\frac{13}{6} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{12}{5})(p+(-13))& =(\color{red}{x}+\color{orange}{\frac{-12}{5}}).(\color{green}{p}+\color{blue}{(-13)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-13)} + \color{orange}{(\frac{-12}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{5})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = px-13x-\frac{12}{5}p+\frac{12}{5}.13& \text{Uitwerken } \\ & =px-13x-\frac{12}{5}p+\frac{156}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-8}{17}+b)(\frac{-8}{8}-p)& =(\color{red}{b}+\color{orange}{\frac{-8}{17}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-8}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1b+\frac{8}{17}p+\frac{8}{17}.1& \text{Uitwerken } \\ & =-bp-1b+\frac{8}{17}p+\frac{8}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-16}{3}-x)(\frac{6}{9}+x)& =(\color{red}{-x}+\color{orange}{\frac{-16}{3}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-16}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{2}{3}x-\frac{16}{3}x-\frac{16}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-x^2+((\frac{-2}{3})+(\frac{-16}{3}))x-\frac{32}{9} & \text{Neem samen} \\ &=-x^2-\frac{18}{3}x-\frac{32}{9} & \text{Maak de som} \\ &=-x^2-6x-\frac{32}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(b+\frac{5}{19})(\frac{-2}{19}+q)& =(\color{red}{b}+\color{orange}{\frac{5}{19}}).(\color{green}{q}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{5}{19})} . \color{green}{(q)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{19}b+\frac{5}{19}q-\frac{5}{19}.\frac{2}{19}& \text{Uitwerken } \\ & =bq-\frac{2}{19}b+\frac{5}{19}q-\frac{10}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{18}+p)(x+\frac{19}{14})& =(\color{red}{p}+\color{orange}{\frac{7}{9}}).(\color{green}{x}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{19}{14}p+\frac{7}{9}x+\frac{7}{9}.\frac{19}{14}& \text{Uitwerken } \\ & =px+\frac{19}{14}p+\frac{7}{9}x+\frac{133}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{19}{14}p+\frac{7}{9}x+\frac{19}{18} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p-\frac{6}{8})(x-\frac{4}{5})& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{x}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{5}p-\frac{3}{4}x+\frac{3}{4}.\frac{4}{5}& \text{Uitwerken } \\ & =px-\frac{4}{5}p-\frac{3}{4}x+\frac{12}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{4}{5}p-\frac{3}{4}x+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
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