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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-16}{19}-p)(p-\frac{-13}{10})& =(\color{red}{-p}+\color{orange}{\frac{-16}{19}}).(\color{green}{p}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{13}{10}p-\frac{16}{19}p-\frac{16}{19}.\frac{13}{10}& \text{Uitwerken } \\ & =-p^2+((\frac{-13}{10})+(\frac{-16}{19}))p-\frac{208}{190} & \text{Neem samen} \\ &=-p^2-\frac{407}{190}p-\frac{208}{190} & \text{Maak de som} \\ &=-p^2-\frac{407}{190}p-\frac{104}{95} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(b-\frac{4}{18})(x+\frac{-20}{3})& =(\color{red}{b}+\color{orange}{\frac{-2}{9}}).(\color{green}{x}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{20}{3}b-\frac{2}{9}x+\frac{2}{9}.\frac{20}{3}& \text{Uitwerken } \\ & =bx-\frac{20}{3}b-\frac{2}{9}x+\frac{40}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{7}{3}-x)(b+\frac{-5}{12})& =(\color{red}{-x}+\color{orange}{\frac{7}{3}}).(\color{green}{b}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{7}{3})} . \color{green}{(b)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{12}x+\frac{7}{3}b-\frac{7}{3}.\frac{5}{12}& \text{Uitwerken } \\ & =-bx+\frac{5}{12}x+\frac{7}{3}b-\frac{35}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{11}{18})(a-\frac{16}{8})& =(\color{red}{b}+\color{orange}{\frac{-11}{18}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-11}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ab-2b-\frac{11}{18}a+\frac{11}{18}.2& \text{Uitwerken } \\ & =ab-2b-\frac{11}{18}a+\frac{22}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-2b-\frac{11}{18}a+\frac{11}{9} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{14}{16}+x)(\frac{14}{12}-b)& =(\color{red}{x}+\color{orange}{\frac{7}{8}}).(\color{green}{-b}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{7}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{6}x-\frac{7}{8}b+\frac{7}{8}.\frac{7}{6}& \text{Uitwerken } \\ & =-bx+\frac{7}{6}x-\frac{7}{8}b+\frac{49}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-19}{17})(b+\frac{18}{7})& =(\color{red}{a}+\color{orange}{\frac{-19}{17}}).(\color{green}{b}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{-19}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{18}{7}a-\frac{19}{17}b-\frac{19}{17}.\frac{18}{7}& \text{Uitwerken } \\ & =ab+\frac{18}{7}a-\frac{19}{17}b-\frac{342}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{20}{12}+b)(\frac{-8}{7}-x)& =(\color{red}{b}+\color{orange}{\frac{5}{3}}).(\color{green}{-x}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{8}{7}b-\frac{5}{3}x-\frac{5}{3}.\frac{8}{7}& \text{Uitwerken } \\ & =-bx-\frac{8}{7}b-\frac{5}{3}x-\frac{40}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{20}{5}+b)(q+\frac{-19}{2})& =(\color{red}{b}+\color{orange}{4}).(\color{green}{q}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{2}b+4q-4.\frac{19}{2}& \text{Uitwerken } \\ & =bq-\frac{19}{2}b+4q-\frac{76}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{19}{2}b+4q-38 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{2}{15}-b)(q+\frac{-12}{5})& =(\color{red}{-b}+\color{orange}{\frac{2}{15}}).(\color{green}{q}+\color{blue}{\frac{-12}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-12}{5})} + \color{orange}{(\frac{2}{15})} . \color{green}{(q)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(\frac{-12}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{12}{5}b+\frac{2}{15}q-\frac{2}{15}.\frac{12}{5}& \text{Uitwerken } \\ & =-bq+\frac{12}{5}b+\frac{2}{15}q-\frac{24}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{12}{5}b+\frac{2}{15}q-\frac{8}{25} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{1}{16}-p)(q-\frac{-4}{9})& =(\color{red}{-p}+\color{orange}{\frac{1}{16}}).(\color{green}{q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{1}{16})} . \color{green}{(q)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{4}{9}p+\frac{1}{16}q+\frac{1}{16}.\frac{4}{9}& \text{Uitwerken } \\ & =-pq-\frac{4}{9}p+\frac{1}{16}q+\frac{4}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{4}{9}p+\frac{1}{16}q+\frac{1}{36} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-8}{10}-p)(\frac{-8}{20}-q)& =(\color{red}{-p}+\color{orange}{\frac{-4}{5}}).(\color{green}{-q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{5}p+\frac{4}{5}q+\frac{4}{5}.\frac{2}{5}& \text{Uitwerken } \\ & =pq+\frac{2}{5}p+\frac{4}{5}q+\frac{8}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{19}{13}+a)(a+\frac{-19}{9})& =(\color{red}{a}+\color{orange}{\frac{19}{13}}).(\color{green}{a}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{19}{13})} . \color{green}{(a)} + \color{orange}{(\frac{19}{13})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{19}{9}a+\frac{19}{13}a-\frac{19}{13}.\frac{19}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-19}{9})+\frac{19}{13})a-(\frac{-361}{117}) & \text{Neem samen} \\ &=a^2-\frac{76}{117}a-(\frac{-361}{117}) & \text{Maak de som} \\\end{align}\)
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