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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{13}{19})(p+\frac{-5}{18})& =(\color{red}{p}+\color{orange}{\frac{13}{19}}).(\color{green}{p}+\color{blue}{\frac{-5}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{18})} + \color{orange}{(\frac{13}{19})} . \color{green}{(p)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{-5}{18})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{18}p+\frac{13}{19}p-\frac{13}{19}.\frac{5}{18}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{18})+\frac{13}{19})p-(\frac{-65}{342}) & \text{Neem samen} \\ &=p^2+\frac{139}{342}p-(\frac{-65}{342}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(b+\frac{4}{19})(\frac{-1}{15}-q)& =(\color{red}{b}+\color{orange}{\frac{4}{19}}).(\color{green}{-q}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{4}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{15}b-\frac{4}{19}q-\frac{4}{19}.\frac{1}{15}& \text{Uitwerken } \\ & =-bq-\frac{1}{15}b-\frac{4}{19}q-\frac{4}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-10}{10})(b-\frac{18}{12})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{2}a+1b-1.\frac{3}{2}& \text{Uitwerken } \\ & =ab-\frac{3}{2}a+1b-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-20}{5})(b+\frac{-3}{5})& =(\color{red}{p}+\color{orange}{4}).(\color{green}{b}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(4)} . \color{green}{(b)} + \color{orange}{(4)} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{5}p+4b-4.\frac{3}{5}& \text{Uitwerken } \\ & =bp-\frac{3}{5}p+4b-\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-14}{8})(q+\frac{-2}{4})& =(\color{red}{a}+\color{orange}{\frac{-7}{4}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{2}a-\frac{7}{4}q+\frac{7}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =aq-\frac{1}{2}a-\frac{7}{4}q+\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{4}{13}+x)(\frac{11}{14}+p)& =(\color{red}{x}+\color{orange}{\frac{4}{13}}).(\color{green}{p}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(\frac{4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{14}x+\frac{4}{13}p+\frac{4}{13}.\frac{11}{14}& \text{Uitwerken } \\ & =px+\frac{11}{14}x+\frac{4}{13}p+\frac{44}{182} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{11}{14}x+\frac{4}{13}p+\frac{22}{91} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a+\frac{2}{3})(x+\frac{-12}{6})& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ax-2a+\frac{2}{3}x-\frac{2}{3}.2& \text{Uitwerken } \\ & =ax-2a+\frac{2}{3}x-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{8}{3}-x)(\frac{2}{19}-q)& =(\color{red}{-x}+\color{orange}{\frac{8}{3}}).(\color{green}{-q}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{8}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{19}x-\frac{8}{3}q+\frac{8}{3}.\frac{2}{19}& \text{Uitwerken } \\ & =qx-\frac{2}{19}x-\frac{8}{3}q+\frac{16}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{8}{8}-x)(x+\frac{-15}{16})& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{15}{16}x+1x-1.\frac{15}{16}& \text{Uitwerken } \\ & =-x^2+(\frac{15}{16}+1)x-\frac{15}{16} & \text{Neem samen} \\ &=-x^2+\frac{31}{16}x-\frac{15}{16} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(b+\frac{14}{5})(\frac{-19}{11}-b)& =(\color{red}{b}+\color{orange}{\frac{14}{5}}).(\color{green}{-b}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{14}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{19}{11}b-\frac{14}{5}b-\frac{14}{5}.\frac{19}{11}& \text{Uitwerken } \\ & =-b^2+((\frac{-19}{11})+(\frac{-14}{5}))b-\frac{266}{55} & \text{Neem samen} \\ &=-b^2-\frac{249}{55}b-\frac{266}{55} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{13}{9}+q)(x-\frac{-15}{19})& =(\color{red}{q}+\color{orange}{\frac{13}{9}}).(\color{green}{x}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(\frac{13}{9})} . \color{green}{(x)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{15}{19}q+\frac{13}{9}x+\frac{13}{9}.\frac{15}{19}& \text{Uitwerken } \\ & =qx+\frac{15}{19}q+\frac{13}{9}x+\frac{195}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{15}{19}q+\frac{13}{9}x+\frac{65}{57} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{18}-x)(q-\frac{-5}{3})& =(\color{red}{-x}+\color{orange}{\frac{4}{9}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{4}{9})} . \color{green}{(q)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{5}{3}x+\frac{4}{9}q+\frac{4}{9}.\frac{5}{3}& \text{Uitwerken } \\ & =-qx-\frac{5}{3}x+\frac{4}{9}q+\frac{20}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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