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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{11}{2})(\frac{11}{19}+b)& =(\color{red}{x}+\color{orange}{\frac{11}{2}}).(\color{green}{b}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{11}{2})} . \color{green}{(b)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{19}x+\frac{11}{2}b+\frac{11}{2}.\frac{11}{19}& \text{Uitwerken } \\ & =bx+\frac{11}{19}x+\frac{11}{2}b+\frac{121}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{3}{4}-q)(\frac{1}{19}+x)& =(\color{red}{-q}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{19}q+\frac{3}{4}x+\frac{3}{4}.\frac{1}{19}& \text{Uitwerken } \\ & =-qx-\frac{1}{19}q+\frac{3}{4}x+\frac{3}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-8}{9})(p+\frac{5}{9})& =(\color{red}{p}+\color{orange}{\frac{-8}{9}}).(\color{green}{p}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{9}p-\frac{8}{9}p-\frac{8}{9}.\frac{5}{9}& \text{Uitwerken } \\ & =p^2+(\frac{5}{9}+(\frac{-8}{9}))p-(\frac{-40}{81}) & \text{Neem samen} \\ &=p^2-\frac{3}{9}p-(\frac{-40}{81}) & \text{Maak de som} \\ &=p^2-\frac{1}{3}p+\frac{40}{81} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(p-\frac{17}{5})(x-\frac{-14}{5})& =(\color{red}{p}+\color{orange}{\frac{-17}{5}}).(\color{green}{x}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{14}{5}p-\frac{17}{5}x-\frac{17}{5}.\frac{14}{5}& \text{Uitwerken } \\ & =px+\frac{14}{5}p-\frac{17}{5}x-\frac{238}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{19}{4})(\frac{-18}{7}+x)& =(\color{red}{q}+\color{orange}{\frac{19}{4}}).(\color{green}{x}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{19}{4})} . \color{green}{(x)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{18}{7}q+\frac{19}{4}x-\frac{19}{4}.\frac{18}{7}& \text{Uitwerken } \\ & =qx-\frac{18}{7}q+\frac{19}{4}x-\frac{342}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{18}{7}q+\frac{19}{4}x-\frac{171}{14} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p+\frac{16}{11})(p-\frac{-2}{13})& =(\color{red}{p}+\color{orange}{\frac{16}{11}}).(\color{green}{p}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{16}{11})} . \color{green}{(p)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{2}{13}p+\frac{16}{11}p+\frac{16}{11}.\frac{2}{13}& \text{Uitwerken } \\ & =p^2+(\frac{2}{13}+\frac{16}{11})p+\frac{32}{143} & \text{Neem samen} \\ &=p^2+\frac{230}{143}p+\frac{32}{143} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-5}{7})(a+\frac{13}{18})& =(\color{red}{q}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{18}q-\frac{5}{7}a-\frac{5}{7}.\frac{13}{18}& \text{Uitwerken } \\ & =aq+\frac{13}{18}q-\frac{5}{7}a-\frac{65}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-5}{13})(\frac{-7}{19}+q)& =(\color{red}{b}+\color{orange}{\frac{5}{13}}).(\color{green}{q}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{5}{13})} . \color{green}{(q)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{19}b+\frac{5}{13}q-\frac{5}{13}.\frac{7}{19}& \text{Uitwerken } \\ & =bq-\frac{7}{19}b+\frac{5}{13}q-\frac{35}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{10}{7})(x+\frac{-3}{5})& =(\color{red}{q}+\color{orange}{\frac{-10}{7}}).(\color{green}{x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{5}q-\frac{10}{7}x+\frac{10}{7}.\frac{3}{5}& \text{Uitwerken } \\ & =qx-\frac{3}{5}q-\frac{10}{7}x+\frac{30}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{3}{5}q-\frac{10}{7}x+\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-18}{19})(\frac{-3}{13}-a)& =(\color{red}{a}+\color{orange}{\frac{-18}{19}}).(\color{green}{-a}+\color{blue}{\frac{-3}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{13})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{-3}{13})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{3}{13}a+\frac{18}{19}a+\frac{18}{19}.\frac{3}{13}& \text{Uitwerken } \\ & =-a^2+((\frac{-3}{13})+\frac{18}{19})a+(\frac{-54}{247}) & \text{Neem samen} \\ &=-a^2+\frac{177}{247}a+(\frac{-54}{247}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-16}{9}+x)(a+\frac{-18}{7})& =(\color{red}{x}+\color{orange}{\frac{-16}{9}}).(\color{green}{a}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{18}{7}x-\frac{16}{9}a+\frac{16}{9}.\frac{18}{7}& \text{Uitwerken } \\ & =ax-\frac{18}{7}x-\frac{16}{9}a+\frac{288}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{18}{7}x-\frac{16}{9}a+\frac{32}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{3}{10}+p)(\frac{-10}{5}-q)& =(\color{red}{p}+\color{orange}{\frac{3}{10}}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{3}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -pq-2p-\frac{3}{10}q-\frac{3}{10}.2& \text{Uitwerken } \\ & =-pq-2p-\frac{3}{10}q-\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-2p-\frac{3}{10}q-\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
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