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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-20}{9})(p-\frac{-7}{6})& =(\color{red}{p}+\color{orange}{\frac{20}{9}}).(\color{green}{p}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{20}{9})} . \color{green}{(p)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{7}{6}p+\frac{20}{9}p+\frac{20}{9}.\frac{7}{6}& \text{Uitwerken } \\ & =p^2+(\frac{7}{6}+\frac{20}{9})p+\frac{140}{54} & \text{Neem samen} \\ &=p^2+\frac{61}{18}p+\frac{140}{54} & \text{Maak de som} \\ &=p^2+\frac{61}{18}p+\frac{70}{27} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{7}-b)(a+\frac{19}{20})& =(\color{red}{-b}+\color{orange}{\frac{20}{7}}).(\color{green}{a}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{20}{7})} . \color{green}{(a)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{19}{20}b+\frac{20}{7}a+\frac{20}{7}.\frac{19}{20}& \text{Uitwerken } \\ & =-ab-\frac{19}{20}b+\frac{20}{7}a+\frac{380}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{19}{20}b+\frac{20}{7}a+\frac{19}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-2}{6}-q)(b+\frac{14}{5})& =(\color{red}{-q}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{14}{5}q-\frac{1}{3}b-\frac{1}{3}.\frac{14}{5}& \text{Uitwerken } \\ & =-bq-\frac{14}{5}q-\frac{1}{3}b-\frac{14}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{16}{15})(b+\frac{-9}{13})& =(\color{red}{q}+\color{orange}{\frac{-16}{15}}).(\color{green}{b}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{9}{13}q-\frac{16}{15}b+\frac{16}{15}.\frac{9}{13}& \text{Uitwerken } \\ & =bq-\frac{9}{13}q-\frac{16}{15}b+\frac{144}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{9}{13}q-\frac{16}{15}b+\frac{48}{65} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{8}+a)(q+\frac{-20}{20})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a-2q+2.1& \text{Uitwerken } \\ & =aq-1a-2q+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-11}{14}-b)(\frac{2}{15}+q)& =(\color{red}{-b}+\color{orange}{\frac{-11}{14}}).(\color{green}{q}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{2}{15}b-\frac{11}{14}q-\frac{11}{14}.\frac{2}{15}& \text{Uitwerken } \\ & =-bq-\frac{2}{15}b-\frac{11}{14}q-\frac{22}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{2}{15}b-\frac{11}{14}q-\frac{11}{105} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-19}{3}-x)(a-\frac{14}{7})& =(\color{red}{-x}+\color{orange}{\frac{-19}{3}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-19}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ax+2x-\frac{19}{3}a+\frac{19}{3}.2& \text{Uitwerken } \\ & =-ax+2x-\frac{19}{3}a+\frac{38}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-16}{2}+p)(p-\frac{-20}{7})& =(\color{red}{p}+\color{orange}{(-8)}).(\color{green}{p}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(-8)} . \color{green}{(p)} + \color{orange}{(-8)} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{20}{7}p-8p-8.\frac{20}{7}& \text{Uitwerken } \\ & =p^2+(\frac{20}{7}+(-8))p-(\frac{-160}{7}) & \text{Neem samen} \\ &=p^2-\frac{36}{7}p-(\frac{-160}{7}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{14}{9}-p)(\frac{10}{10}+q)& =(\color{red}{-p}+\color{orange}{\frac{14}{9}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{14}{9})} . \color{green}{(q)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -pq-1p+\frac{14}{9}q+\frac{14}{9}.1& \text{Uitwerken } \\ & =-pq-1p+\frac{14}{9}q+\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-12}{2}-q)(p-\frac{-8}{13})& =(\color{red}{-q}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{8}{13}q-6p-6.\frac{8}{13}& \text{Uitwerken } \\ & =-pq-\frac{8}{13}q-6p-\frac{48}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-8}{4}+q)(\frac{13}{4}+x)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{4}q-2x-2.\frac{13}{4}& \text{Uitwerken } \\ & =qx+\frac{13}{4}q-2x-\frac{26}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{13}{4}q-2x-\frac{13}{2} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-8}{14}-b)(a-\frac{-2}{19})& =(\color{red}{-b}+\color{orange}{\frac{-4}{7}}).(\color{green}{a}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{19}b-\frac{4}{7}a-\frac{4}{7}.\frac{2}{19}& \text{Uitwerken } \\ & =-ab-\frac{2}{19}b-\frac{4}{7}a-\frac{8}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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