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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{20}-q)(\frac{-11}{6}-a)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{6}q-1a-1.\frac{11}{6}& \text{Uitwerken } \\ & =aq+\frac{11}{6}q-1a-\frac{11}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-5}{6})(q+\frac{-6}{13})& =(\color{red}{p}+\color{orange}{\frac{5}{6}}).(\color{green}{q}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{6}{13}p+\frac{5}{6}q-\frac{5}{6}.\frac{6}{13}& \text{Uitwerken } \\ & =pq-\frac{6}{13}p+\frac{5}{6}q-\frac{30}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{6}{13}p+\frac{5}{6}q-\frac{5}{13} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{13}{20}-p)(\frac{9}{3}-b)& =(\color{red}{-p}+\color{orange}{\frac{13}{20}}).(\color{green}{-b}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(3)} + \color{orange}{(\frac{13}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bp-3p-\frac{13}{20}b+\frac{13}{20}.3& \text{Uitwerken } \\ & =bp-3p-\frac{13}{20}b+\frac{39}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-17}{5})(\frac{6}{8}-x)& =(\color{red}{a}+\color{orange}{\frac{17}{5}}).(\color{green}{-x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{17}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{4}a-\frac{17}{5}x+\frac{17}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =-ax+\frac{3}{4}a-\frac{17}{5}x+\frac{51}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{9}{5})(q-16)& =(\color{red}{a}+\color{orange}{\frac{9}{5}}).(\color{green}{q}+\color{blue}{(-16)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-16)} + \color{orange}{(\frac{9}{5})} . \color{green}{(q)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = aq-16a+\frac{9}{5}q-\frac{9}{5}.16& \text{Uitwerken } \\ & =aq-16a+\frac{9}{5}q-\frac{144}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{13}{12}-q)(\frac{20}{5}-a)& =(\color{red}{-q}+\color{orange}{\frac{13}{12}}).(\color{green}{-a}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(4)} + \color{orange}{(\frac{13}{12})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = aq-4q-\frac{13}{12}a+\frac{13}{12}.4& \text{Uitwerken } \\ & =aq-4q-\frac{13}{12}a+\frac{52}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-4q-\frac{13}{12}a+\frac{13}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-11}{15})(\frac{-20}{17}-p)& =(\color{red}{q}+\color{orange}{\frac{-11}{15}}).(\color{green}{-p}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{20}{17}q+\frac{11}{15}p+\frac{11}{15}.\frac{20}{17}& \text{Uitwerken } \\ & =-pq-\frac{20}{17}q+\frac{11}{15}p+\frac{220}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{20}{17}q+\frac{11}{15}p+\frac{44}{51} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}((-19)-b)(q+\frac{11}{19})& =(\color{red}{-b}+\color{orange}{(-19)}).(\color{green}{q}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(-19)} . \color{green}{(q)} + \color{orange}{(-19)} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{11}{19}b-19q-19.\frac{11}{19}& \text{Uitwerken } \\ & =-bq-\frac{11}{19}b-19q-\frac{209}{19} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{11}{19}b-19q-11 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-15}{3}+q)(\frac{-5}{5}+b)& =(\color{red}{q}+\color{orange}{(-5)}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(-5)} . \color{green}{(b)} + \color{orange}{(-5)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq-1q-5b+5.1& \text{Uitwerken } \\ & =bq-1q-5b+5 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-1}{10})(\frac{13}{5}-a)& =(\color{red}{p}+\color{orange}{\frac{1}{10}}).(\color{green}{-a}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{1}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{5}p-\frac{1}{10}a+\frac{1}{10}.\frac{13}{5}& \text{Uitwerken } \\ & =-ap+\frac{13}{5}p-\frac{1}{10}a+\frac{13}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{5}+b)(p-\frac{1}{20})& =(\color{red}{b}+\color{orange}{\frac{16}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{16}{5})} . \color{green}{(p)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{20}b+\frac{16}{5}p-\frac{16}{5}.\frac{1}{20}& \text{Uitwerken } \\ & =bp-\frac{1}{20}b+\frac{16}{5}p-\frac{16}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{1}{20}b+\frac{16}{5}p-\frac{4}{25} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-13}{15})(p-\frac{14}{19})& =(\color{red}{q}+\color{orange}{\frac{-13}{15}}).(\color{green}{p}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{14}{19}q-\frac{13}{15}p+\frac{13}{15}.\frac{14}{19}& \text{Uitwerken } \\ & =pq-\frac{14}{19}q-\frac{13}{15}p+\frac{182}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-17 22:50:29
Een site van Busleyden Atheneum Mechelen