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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-16}{15}-p)(\frac{1}{6}+q)& =(\color{red}{-p}+\color{orange}{\frac{-16}{15}}).(\color{green}{q}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{6}p-\frac{16}{15}q-\frac{16}{15}.\frac{1}{6}& \text{Uitwerken } \\ & =-pq-\frac{1}{6}p-\frac{16}{15}q-\frac{16}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{1}{6}p-\frac{16}{15}q-\frac{8}{45} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q+\frac{8}{12})(q-\frac{-15}{19})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{15}{19}q+\frac{2}{3}q+\frac{2}{3}.\frac{15}{19}& \text{Uitwerken } \\ & =q^2+(\frac{15}{19}+\frac{2}{3})q+\frac{30}{57} & \text{Neem samen} \\ &=q^2+\frac{83}{57}q+\frac{30}{57} & \text{Maak de som} \\ &=q^2+\frac{83}{57}q+\frac{10}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(q-\frac{5}{7})(a-\frac{8}{14})& =(\color{red}{q}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{7}q-\frac{5}{7}a+\frac{5}{7}.\frac{4}{7}& \text{Uitwerken } \\ & =aq-\frac{4}{7}q-\frac{5}{7}a+\frac{20}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-5}{5})(\frac{-14}{15}+a)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{14}{15}b-1a+1.\frac{14}{15}& \text{Uitwerken } \\ & =ab-\frac{14}{15}b-1a+\frac{14}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p+\frac{2}{6})(q-\frac{-14}{12})& =(\color{red}{p}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{6}p+\frac{1}{3}q+\frac{1}{3}.\frac{7}{6}& \text{Uitwerken } \\ & =pq+\frac{7}{6}p+\frac{1}{3}q+\frac{7}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{18}{11})(\frac{17}{8}+q)& =(\color{red}{a}+\color{orange}{\frac{-18}{11}}).(\color{green}{q}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{-18}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{11})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{8}a-\frac{18}{11}q-\frac{18}{11}.\frac{17}{8}& \text{Uitwerken } \\ & =aq+\frac{17}{8}a-\frac{18}{11}q-\frac{306}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{17}{8}a-\frac{18}{11}q-\frac{153}{44} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-8}{20})(8-a)& =(\color{red}{p}+\color{orange}{\frac{2}{5}}).(\color{green}{-a}+\color{blue}{8})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(8)} + \color{orange}{(\frac{2}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = -ap+8p-\frac{2}{5}a+\frac{2}{5}.8& \text{Uitwerken } \\ & =-ap+8p-\frac{2}{5}a+\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-8}{15}-q)(\frac{20}{3}+q)& =(\color{red}{-q}+\color{orange}{\frac{-8}{15}}).(\color{green}{q}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{20}{3}q-\frac{8}{15}q-\frac{8}{15}.\frac{20}{3}& \text{Uitwerken } \\ & =-q^2+((\frac{-20}{3})+(\frac{-8}{15}))q-\frac{160}{45} & \text{Neem samen} \\ &=-q^2-\frac{108}{15}q-\frac{160}{45} & \text{Maak de som} \\ &=-q^2-\frac{36}{5}q-\frac{32}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{19}{9}-p)(\frac{11}{20}-q)& =(\color{red}{-p}+\color{orange}{\frac{19}{9}}).(\color{green}{-q}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{19}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{20}p-\frac{19}{9}q+\frac{19}{9}.\frac{11}{20}& \text{Uitwerken } \\ & =pq-\frac{11}{20}p-\frac{19}{9}q+\frac{209}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{15}{2}-p)(p-\frac{-12}{10})& =(\color{red}{-p}+\color{orange}{\frac{15}{2}}).(\color{green}{p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{15}{2})} . \color{green}{(p)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{6}{5}p+\frac{15}{2}p+\frac{15}{2}.\frac{6}{5}& \text{Uitwerken } \\ & =-p^2+((\frac{-6}{5})+\frac{15}{2})p+(\frac{-90}{10}) & \text{Neem samen} \\ &=-p^2+\frac{63}{10}p+(\frac{-90}{10}) & \text{Maak de som} \\ &=-p^2+\frac{63}{10}p+(-9) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-16}{11}-p)(\frac{16}{11}+a)& =(\color{red}{-p}+\color{orange}{\frac{-16}{11}}).(\color{green}{a}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{16}{11}p-\frac{16}{11}a-\frac{16}{11}.\frac{16}{11}& \text{Uitwerken } \\ & =-ap-\frac{16}{11}p-\frac{16}{11}a-\frac{256}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-13}{3}+x)(\frac{15}{3}+p)& =(\color{red}{x}+\color{orange}{\frac{-13}{3}}).(\color{green}{p}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(5)} + \color{orange}{(\frac{-13}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = px+5x-\frac{13}{3}p-\frac{13}{3}.5& \text{Uitwerken } \\ & =px+5x-\frac{13}{3}p-\frac{65}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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