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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{5}{14})(a+\frac{-18}{12})& =(\color{red}{x}+\color{orange}{\frac{-5}{14}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{2}x-\frac{5}{14}a+\frac{5}{14}.\frac{3}{2}& \text{Uitwerken } \\ & =ax-\frac{3}{2}x-\frac{5}{14}a+\frac{15}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-19}{12}-x)(\frac{-12}{16}-p)& =(\color{red}{-x}+\color{orange}{\frac{-19}{12}}).(\color{green}{-p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{4}x+\frac{19}{12}p+\frac{19}{12}.\frac{3}{4}& \text{Uitwerken } \\ & =px+\frac{3}{4}x+\frac{19}{12}p+\frac{57}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{3}{4}x+\frac{19}{12}p+\frac{19}{16} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-3}{7}-b)(\frac{19}{6}+a)& =(\color{red}{-b}+\color{orange}{\frac{-3}{7}}).(\color{green}{a}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{19}{6}b-\frac{3}{7}a-\frac{3}{7}.\frac{19}{6}& \text{Uitwerken } \\ & =-ab-\frac{19}{6}b-\frac{3}{7}a-\frac{57}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{19}{6}b-\frac{3}{7}a-\frac{19}{14} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-4}{17}+x)(\frac{-14}{14}-x)& =(\color{red}{x}+\color{orange}{\frac{-4}{17}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-4}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -xx-1x+\frac{4}{17}x+\frac{4}{17}.1& \text{Uitwerken } \\ & =-x^2+((-1)+\frac{4}{17})x+(\frac{-4}{17}) & \text{Neem samen} \\ &=-x^2-\frac{13}{17}x+(\frac{-4}{17}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{11}{9}-p)(\frac{-15}{19}+x)& =(\color{red}{-p}+\color{orange}{\frac{11}{9}}).(\color{green}{x}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{11}{9})} . \color{green}{(x)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{15}{19}p+\frac{11}{9}x-\frac{11}{9}.\frac{15}{19}& \text{Uitwerken } \\ & =-px+\frac{15}{19}p+\frac{11}{9}x-\frac{165}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{15}{19}p+\frac{11}{9}x-\frac{55}{57} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}((-8)-q)(\frac{7}{9}-b)& =(\color{red}{-q}+\color{orange}{(-8)}).(\color{green}{-b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(-8)} . \color{green}{(-b)} + \color{orange}{(-8)} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{9}q+8b-8.\frac{7}{9}& \text{Uitwerken } \\ & =bq-\frac{7}{9}q+8b-\frac{56}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{9}{10})(p+\frac{18}{9})& =(\color{red}{a}+\color{orange}{\frac{-9}{10}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-9}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2a-\frac{9}{10}p-\frac{9}{10}.2& \text{Uitwerken } \\ & =ap+2a-\frac{9}{10}p-\frac{18}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+2a-\frac{9}{10}p-\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-15}{13})(b-\frac{-4}{2})& =(\color{red}{a}+\color{orange}{\frac{15}{13}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{15}{13})} . \color{green}{(b)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ab+2a+\frac{15}{13}b+\frac{15}{13}.2& \text{Uitwerken } \\ & =ab+2a+\frac{15}{13}b+\frac{30}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{20}{9})(\frac{-13}{7}+q)& =(\color{red}{x}+\color{orange}{\frac{-20}{9}}).(\color{green}{q}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{-20}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{7}x-\frac{20}{9}q+\frac{20}{9}.\frac{13}{7}& \text{Uitwerken } \\ & =qx-\frac{13}{7}x-\frac{20}{9}q+\frac{260}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-11}{10}+q)(q+\frac{9}{14})& =(\color{red}{q}+\color{orange}{\frac{-11}{10}}).(\color{green}{q}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(\frac{-11}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{9}{14}q-\frac{11}{10}q-\frac{11}{10}.\frac{9}{14}& \text{Uitwerken } \\ & =q^2+(\frac{9}{14}+(\frac{-11}{10}))q-(\frac{-99}{140}) & \text{Neem samen} \\ &=q^2-\frac{32}{70}q-(\frac{-99}{140}) & \text{Maak de som} \\ &=q^2-\frac{16}{35}q+\frac{99}{140} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-6}{3})(b+\frac{-9}{4})& =(\color{red}{q}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{9}{4}q+2b-2.\frac{9}{4}& \text{Uitwerken } \\ & =bq-\frac{9}{4}q+2b-\frac{18}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{9}{4}q+2b-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-\frac{13}{8})(\frac{-5}{5}+x)& =(\color{red}{b}+\color{orange}{\frac{-13}{8}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-13}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx-1b-\frac{13}{8}x+\frac{13}{8}.1& \text{Uitwerken } \\ & =bx-1b-\frac{13}{8}x+\frac{13}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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