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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{16}{5})(\frac{2}{11}-p)& =(\color{red}{b}+\color{orange}{\frac{-16}{5}}).(\color{green}{-p}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{2}{11}b+\frac{16}{5}p-\frac{16}{5}.\frac{2}{11}& \text{Uitwerken } \\ & =-bp+\frac{2}{11}b+\frac{16}{5}p-\frac{32}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{8}{14})(q-\frac{-16}{10})& =(\color{red}{p}+\color{orange}{\frac{-4}{7}}).(\color{green}{q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{5}p-\frac{4}{7}q-\frac{4}{7}.\frac{8}{5}& \text{Uitwerken } \\ & =pq+\frac{8}{5}p-\frac{4}{7}q-\frac{32}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-2}{3})(p-\frac{-18}{19})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{18}{19}p+\frac{2}{3}p+\frac{2}{3}.\frac{18}{19}& \text{Uitwerken } \\ & =p^2+(\frac{18}{19}+\frac{2}{3})p+\frac{36}{57} & \text{Neem samen} \\ &=p^2+\frac{92}{57}p+\frac{36}{57} & \text{Maak de som} \\ &=p^2+\frac{92}{57}p+\frac{12}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{-2}{19}-a)(\frac{-3}{6}-p)& =(\color{red}{-a}+\color{orange}{\frac{-2}{19}}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-2}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{2}a+\frac{2}{19}p+\frac{2}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =ap+\frac{1}{2}a+\frac{2}{19}p+\frac{2}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{2}a+\frac{2}{19}p+\frac{1}{19} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{1}{7}-a)(\frac{15}{14}+q)& =(\color{red}{-a}+\color{orange}{\frac{1}{7}}).(\color{green}{q}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{15}{14}a+\frac{1}{7}q+\frac{1}{7}.\frac{15}{14}& \text{Uitwerken } \\ & =-aq-\frac{15}{14}a+\frac{1}{7}q+\frac{15}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{1}{9}-q)(\frac{-19}{18}+x)& =(\color{red}{-q}+\color{orange}{\frac{1}{9}}).(\color{green}{x}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{1}{9})} . \color{green}{(x)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{19}{18}q+\frac{1}{9}x-\frac{1}{9}.\frac{19}{18}& \text{Uitwerken } \\ & =-qx+\frac{19}{18}q+\frac{1}{9}x-\frac{19}{162} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-20}{2})(\frac{7}{14}+a)& =(\color{red}{p}+\color{orange}{10}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(10)} . \color{green}{(a)} + \color{orange}{(10)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{2}p+10a+10.\frac{1}{2}& \text{Uitwerken } \\ & =ap+\frac{1}{2}p+10a+\frac{10}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{2}p+10a+5 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{15}{7})(\frac{-14}{17}-b)& =(\color{red}{p}+\color{orange}{\frac{15}{7}}).(\color{green}{-b}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{15}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{14}{17}p-\frac{15}{7}b-\frac{15}{7}.\frac{14}{17}& \text{Uitwerken } \\ & =-bp-\frac{14}{17}p-\frac{15}{7}b-\frac{210}{119} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{14}{17}p-\frac{15}{7}b-\frac{30}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{1}{10}-q)(b-\frac{-18}{14})& =(\color{red}{-q}+\color{orange}{\frac{1}{10}}).(\color{green}{b}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{1}{10})} . \color{green}{(b)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{7}q+\frac{1}{10}b+\frac{1}{10}.\frac{9}{7}& \text{Uitwerken } \\ & =-bq-\frac{9}{7}q+\frac{1}{10}b+\frac{9}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-16}{5}+a)(\frac{3}{9}-q)& =(\color{red}{a}+\color{orange}{\frac{-16}{5}}).(\color{green}{-q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{3}a+\frac{16}{5}q-\frac{16}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =-aq+\frac{1}{3}a+\frac{16}{5}q-\frac{16}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-5}{14}-p)(\frac{16}{4}+a)& =(\color{red}{-p}+\color{orange}{\frac{-5}{14}}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(4)} + \color{orange}{(\frac{-5}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -ap-4p-\frac{5}{14}a-\frac{5}{14}.4& \text{Uitwerken } \\ & =-ap-4p-\frac{5}{14}a-\frac{20}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-4p-\frac{5}{14}a-\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{6}{11}-b)(q-\frac{-13}{4})& =(\color{red}{-b}+\color{orange}{\frac{6}{11}}).(\color{green}{q}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{6}{11})} . \color{green}{(q)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{4}b+\frac{6}{11}q+\frac{6}{11}.\frac{13}{4}& \text{Uitwerken } \\ & =-bq-\frac{13}{4}b+\frac{6}{11}q+\frac{78}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{13}{4}b+\frac{6}{11}q+\frac{39}{22} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-01 17:21:21
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