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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-7}{2})(\frac{3}{5}+a)& =(\color{red}{q}+\color{orange}{\frac{-7}{2}}).(\color{green}{a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{5}q-\frac{7}{2}a-\frac{7}{2}.\frac{3}{5}& \text{Uitwerken } \\ & =aq+\frac{3}{5}q-\frac{7}{2}a-\frac{21}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-19}{13})(x+\frac{-3}{3})& =(\color{red}{q}+\color{orange}{\frac{-19}{13}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-19}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1q-\frac{19}{13}x+\frac{19}{13}.1& \text{Uitwerken } \\ & =qx-1q-\frac{19}{13}x+\frac{19}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-3}{7}-a)(x-\frac{-2}{15})& =(\color{red}{-a}+\color{orange}{\frac{-3}{7}}).(\color{green}{x}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{2}{15}a-\frac{3}{7}x-\frac{3}{7}.\frac{2}{15}& \text{Uitwerken } \\ & =-ax-\frac{2}{15}a-\frac{3}{7}x-\frac{6}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{2}{15}a-\frac{3}{7}x-\frac{2}{35} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{19}{2}+a)(x-\frac{-20}{13})& =(\color{red}{a}+\color{orange}{\frac{19}{2}}).(\color{green}{x}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{19}{2})} . \color{green}{(x)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{20}{13}a+\frac{19}{2}x+\frac{19}{2}.\frac{20}{13}& \text{Uitwerken } \\ & =ax+\frac{20}{13}a+\frac{19}{2}x+\frac{380}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{20}{13}a+\frac{19}{2}x+\frac{190}{13} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-4}{7}-a)(a+\frac{19}{12})& =(\color{red}{-a}+\color{orange}{\frac{-4}{7}}).(\color{green}{a}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{19}{12}a-\frac{4}{7}a-\frac{4}{7}.\frac{19}{12}& \text{Uitwerken } \\ & =-a^2+((\frac{-19}{12})+(\frac{-4}{7}))a-\frac{76}{84} & \text{Neem samen} \\ &=-a^2-\frac{181}{84}a-\frac{76}{84} & \text{Maak de som} \\ &=-a^2-\frac{181}{84}a-\frac{19}{21} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-2}{7})(q-\frac{-6}{10})& =(\color{red}{p}+\color{orange}{\frac{-2}{7}}).(\color{green}{q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{5}p-\frac{2}{7}q-\frac{2}{7}.\frac{3}{5}& \text{Uitwerken } \\ & =pq+\frac{3}{5}p-\frac{2}{7}q-\frac{6}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-14}{6})(b-\frac{3}{20})& =(\color{red}{b}+\color{orange}{\frac{-7}{3}}).(\color{green}{b}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{20}b-\frac{7}{3}b+\frac{7}{3}.\frac{3}{20}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{20})+(\frac{-7}{3}))b+\frac{21}{60} & \text{Neem samen} \\ &=b^2-\frac{149}{60}b+\frac{21}{60} & \text{Maak de som} \\ &=b^2-\frac{149}{60}b+\frac{7}{20} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(q+\frac{3}{11})(q+\frac{-11}{4})& =(\color{red}{q}+\color{orange}{\frac{3}{11}}).(\color{green}{q}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{3}{11})} . \color{green}{(q)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{4}q+\frac{3}{11}q-\frac{3}{11}.\frac{11}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{4})+\frac{3}{11})q-(\frac{-33}{44}) & \text{Neem samen} \\ &=q^2-\frac{109}{44}q-(\frac{-33}{44}) & \text{Maak de som} \\ &=q^2-\frac{109}{44}q+\frac{3}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(b-\frac{8}{16})(\frac{18}{17}-q)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{-q}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{18}{17}b+\frac{1}{2}q-\frac{1}{2}.\frac{18}{17}& \text{Uitwerken } \\ & =-bq+\frac{18}{17}b+\frac{1}{2}q-\frac{18}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{18}{17}b+\frac{1}{2}q-\frac{9}{17} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-16}{14})(x-\frac{8}{11})& =(\color{red}{x}+\color{orange}{\frac{8}{7}}).(\color{green}{x}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(\frac{8}{7})} . \color{green}{(x)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{8}{11}x+\frac{8}{7}x-\frac{8}{7}.\frac{8}{11}& \text{Uitwerken } \\ & =x^2+((\frac{-8}{11})+\frac{8}{7})x-(\frac{-64}{77}) & \text{Neem samen} \\ &=x^2+\frac{32}{77}x-(\frac{-64}{77}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-19}{8})(\frac{6}{17}+p)& =(\color{red}{b}+\color{orange}{\frac{-19}{8}}).(\color{green}{p}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{-19}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{6}{17}b-\frac{19}{8}p-\frac{19}{8}.\frac{6}{17}& \text{Uitwerken } \\ & =bp+\frac{6}{17}b-\frac{19}{8}p-\frac{114}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{6}{17}b-\frac{19}{8}p-\frac{57}{68} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x-\frac{8}{4})(q+\frac{-19}{14})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{14}x-2q+2.\frac{19}{14}& \text{Uitwerken } \\ & =qx-\frac{19}{14}x-2q+\frac{38}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{19}{14}x-2q+\frac{19}{7} & \text{Vereenvoudig} \\\end{align}\)
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