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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-6}{18}-a)(x-\frac{5}{11})& =(\color{red}{-a}+\color{orange}{\frac{-1}{3}}).(\color{green}{x}+\color{blue}{\frac{-5}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{11})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-5}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{11}a-\frac{1}{3}x+\frac{1}{3}.\frac{5}{11}& \text{Uitwerken } \\ & =-ax+\frac{5}{11}a-\frac{1}{3}x+\frac{5}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-18}{17})(a-(-17))& =(\color{red}{a}+\color{orange}{\frac{18}{17}}).(\color{green}{a}+\color{blue}{17})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(17)} + \color{orange}{(\frac{18}{17})} . \color{green}{(a)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = aa+17a+\frac{18}{17}a+\frac{18}{17}.17& \text{Uitwerken } \\ & =a^2+(17+\frac{18}{17})a+\frac{306}{17} & \text{Neem samen} \\ &=a^2+\frac{307}{17}a+\frac{306}{17} & \text{Maak de som} \\ &=a^2+\frac{307}{17}a+18 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{11}{20}+a)(\frac{-1}{7}+q)& =(\color{red}{a}+\color{orange}{\frac{11}{20}}).(\color{green}{q}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{11}{20})} . \color{green}{(q)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{7}a+\frac{11}{20}q-\frac{11}{20}.\frac{1}{7}& \text{Uitwerken } \\ & =aq-\frac{1}{7}a+\frac{11}{20}q-\frac{11}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{1}{19})(b-\frac{-14}{8})& =(\color{red}{x}+\color{orange}{\frac{1}{19}}).(\color{green}{b}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{1}{19})} . \color{green}{(b)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{4}x+\frac{1}{19}b+\frac{1}{19}.\frac{7}{4}& \text{Uitwerken } \\ & =bx+\frac{7}{4}x+\frac{1}{19}b+\frac{7}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{12}{19}+p)(q-\frac{10}{2})& =(\color{red}{p}+\color{orange}{\frac{12}{19}}).(\color{green}{q}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(\frac{12}{19})} . \color{green}{(q)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = pq-5p+\frac{12}{19}q-\frac{12}{19}.5& \text{Uitwerken } \\ & =pq-5p+\frac{12}{19}q-\frac{60}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-19}{15}+p)(\frac{-16}{17}-q)& =(\color{red}{p}+\color{orange}{\frac{-19}{15}}).(\color{green}{-q}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{-19}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{16}{17}p+\frac{19}{15}q+\frac{19}{15}.\frac{16}{17}& \text{Uitwerken } \\ & =-pq-\frac{16}{17}p+\frac{19}{15}q+\frac{304}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{17}+x)(\frac{-19}{3}-a)& =(\color{red}{x}+\color{orange}{\frac{8}{17}}).(\color{green}{-a}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{8}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{19}{3}x-\frac{8}{17}a-\frac{8}{17}.\frac{19}{3}& \text{Uitwerken } \\ & =-ax-\frac{19}{3}x-\frac{8}{17}a-\frac{152}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{19}{12})(x+\frac{18}{12})& =(\color{red}{p}+\color{orange}{\frac{19}{12}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{19}{12})} . \color{green}{(x)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{2}p+\frac{19}{12}x+\frac{19}{12}.\frac{3}{2}& \text{Uitwerken } \\ & =px+\frac{3}{2}p+\frac{19}{12}x+\frac{57}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{3}{2}p+\frac{19}{12}x+\frac{19}{8} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{18}{9})(\frac{-11}{10}-q)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{-q}+\color{blue}{\frac{-11}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{10})} + \color{orange}{(-2)} . \color{green}{(-q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-11}{10})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{11}{10}p+2q+2.\frac{11}{10}& \text{Uitwerken } \\ & =-pq-\frac{11}{10}p+2q+\frac{22}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{11}{10}p+2q+\frac{11}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-6}{17})(p-\frac{10}{6})& =(\color{red}{p}+\color{orange}{\frac{6}{17}}).(\color{green}{p}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{6}{17})} . \color{green}{(p)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{3}p+\frac{6}{17}p-\frac{6}{17}.\frac{5}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{3})+\frac{6}{17})p-(\frac{-30}{51}) & \text{Neem samen} \\ &=p^2-\frac{67}{51}p-(\frac{-30}{51}) & \text{Maak de som} \\ &=p^2-\frac{67}{51}p+\frac{10}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-4}{20})(\frac{12}{13}-x)& =(\color{red}{x}+\color{orange}{\frac{1}{5}}).(\color{green}{-x}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{12}{13}x-\frac{1}{5}x+\frac{1}{5}.\frac{12}{13}& \text{Uitwerken } \\ & =-x^2+(\frac{12}{13}+(\frac{-1}{5}))x+(\frac{-12}{65}) & \text{Neem samen} \\ &=-x^2+\frac{47}{65}x+(\frac{-12}{65}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-16}{10})(\frac{-11}{3}-q)& =(\color{red}{q}+\color{orange}{\frac{-8}{5}}).(\color{green}{-q}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{11}{3}q+\frac{8}{5}q+\frac{8}{5}.\frac{11}{3}& \text{Uitwerken } \\ & =-q^2+((\frac{-11}{3})+\frac{8}{5})q+(\frac{-88}{15}) & \text{Neem samen} \\ &=-q^2-\frac{31}{15}q+(\frac{-88}{15}) & \text{Maak de som} \\\end{align}\)
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