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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-4}{10}-b)(\frac{8}{18}+q)& =(\color{red}{-b}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{4}{9}b-\frac{2}{5}q-\frac{2}{5}.\frac{4}{9}& \text{Uitwerken } \\ & =-bq-\frac{4}{9}b-\frac{2}{5}q-\frac{8}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{14}{11}+b)(\frac{17}{12}+q)& =(\color{red}{b}+\color{orange}{\frac{14}{11}}).(\color{green}{q}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{14}{11})} . \color{green}{(q)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{12}b+\frac{14}{11}q+\frac{14}{11}.\frac{17}{12}& \text{Uitwerken } \\ & =bq+\frac{17}{12}b+\frac{14}{11}q+\frac{238}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{17}{12}b+\frac{14}{11}q+\frac{119}{66} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+\frac{6}{19})(b-\frac{-3}{2})& =(\color{red}{b}+\color{orange}{\frac{6}{19}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{6}{19})} . \color{green}{(b)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{2}b+\frac{6}{19}b+\frac{6}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =b^2+(\frac{3}{2}+\frac{6}{19})b+\frac{18}{38} & \text{Neem samen} \\ &=b^2+\frac{69}{38}b+\frac{18}{38} & \text{Maak de som} \\ &=b^2+\frac{69}{38}b+\frac{9}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{18}{10}-a)(a+\frac{-5}{9})& =(\color{red}{-a}+\color{orange}{\frac{9}{5}}).(\color{green}{a}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{9}{5})} . \color{green}{(a)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{5}{9}a+\frac{9}{5}a-\frac{9}{5}.\frac{5}{9}& \text{Uitwerken } \\ & =-a^2+(\frac{5}{9}+\frac{9}{5})a-\frac{45}{45} & \text{Neem samen} \\ &=-a^2+\frac{106}{45}a-\frac{45}{45} & \text{Maak de som} \\ &=-a^2+\frac{106}{45}a-1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(x-\frac{18}{14})(\frac{15}{3}+q)& =(\color{red}{x}+\color{orange}{\frac{-9}{7}}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(5)} + \color{orange}{(\frac{-9}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = qx+5x-\frac{9}{7}q-\frac{9}{7}.5& \text{Uitwerken } \\ & =qx+5x-\frac{9}{7}q-\frac{45}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-1}{15}-p)(b+\frac{20}{19})& =(\color{red}{-p}+\color{orange}{\frac{-1}{15}}).(\color{green}{b}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{20}{19}p-\frac{1}{15}b-\frac{1}{15}.\frac{20}{19}& \text{Uitwerken } \\ & =-bp-\frac{20}{19}p-\frac{1}{15}b-\frac{20}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{20}{19}p-\frac{1}{15}b-\frac{4}{57} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-13}{2}-b)(q-\frac{3}{11})& =(\color{red}{-b}+\color{orange}{\frac{-13}{2}}).(\color{green}{q}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{11}b-\frac{13}{2}q+\frac{13}{2}.\frac{3}{11}& \text{Uitwerken } \\ & =-bq+\frac{3}{11}b-\frac{13}{2}q+\frac{39}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-17}{15})(x+\frac{-1}{14})& =(\color{red}{a}+\color{orange}{\frac{17}{15}}).(\color{green}{x}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{17}{15})} . \color{green}{(x)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{14}a+\frac{17}{15}x-\frac{17}{15}.\frac{1}{14}& \text{Uitwerken } \\ & =ax-\frac{1}{14}a+\frac{17}{15}x-\frac{17}{210} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-6}{13})(\frac{16}{5}-q)& =(\color{red}{b}+\color{orange}{\frac{-6}{13}}).(\color{green}{-q}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{16}{5}b+\frac{6}{13}q-\frac{6}{13}.\frac{16}{5}& \text{Uitwerken } \\ & =-bq+\frac{16}{5}b+\frac{6}{13}q-\frac{96}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{14}{10})(\frac{-16}{13}+q)& =(\color{red}{p}+\color{orange}{\frac{7}{5}}).(\color{green}{q}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{16}{13}p+\frac{7}{5}q-\frac{7}{5}.\frac{16}{13}& \text{Uitwerken } \\ & =pq-\frac{16}{13}p+\frac{7}{5}q-\frac{112}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-3}{4}+p)(p+\frac{-18}{9})& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pp-2p-\frac{3}{4}p+\frac{3}{4}.2& \text{Uitwerken } \\ & =p^2+((-2)+(\frac{-3}{4}))p+\frac{6}{4} & \text{Neem samen} \\ &=p^2-\frac{11}{4}p+\frac{6}{4} & \text{Maak de som} \\ &=p^2-\frac{11}{4}p+\frac{3}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(q+\frac{8}{11})(\frac{9}{8}+x)& =(\color{red}{q}+\color{orange}{\frac{8}{11}}).(\color{green}{x}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{8}{11})} . \color{green}{(x)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{8}q+\frac{8}{11}x+\frac{8}{11}.\frac{9}{8}& \text{Uitwerken } \\ & =qx+\frac{9}{8}q+\frac{8}{11}x+\frac{72}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{9}{8}q+\frac{8}{11}x+\frac{9}{11} & \text{Vereenvoudig} \\\end{align}\)
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