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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{4}+p)(\frac{-13}{19}-x)& =(\color{red}{p}+\color{orange}{5}).(\color{green}{-x}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(5)} . \color{green}{(-x)} + \color{orange}{(5)} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{13}{19}p-5x-5.\frac{13}{19}& \text{Uitwerken } \\ & =-px-\frac{13}{19}p-5x-\frac{65}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-17}{12}+a)(b+\frac{9}{2})& =(\color{red}{a}+\color{orange}{\frac{-17}{12}}).(\color{green}{b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{2}a-\frac{17}{12}b-\frac{17}{12}.\frac{9}{2}& \text{Uitwerken } \\ & =ab+\frac{9}{2}a-\frac{17}{12}b-\frac{153}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{9}{2}a-\frac{17}{12}b-\frac{51}{8} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}((-1)-a)(\frac{-11}{5}+b)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{11}{5}a-1b+1.\frac{11}{5}& \text{Uitwerken } \\ & =-ab+\frac{11}{5}a-1b+\frac{11}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{13}{14})((-16)-a)& =(\color{red}{q}+\color{orange}{\frac{-13}{14}}).(\color{green}{-a}+\color{blue}{(-16)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-16)} + \color{orange}{(\frac{-13}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = -aq-16q+\frac{13}{14}a+\frac{13}{14}.16& \text{Uitwerken } \\ & =-aq-16q+\frac{13}{14}a+\frac{208}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-16q+\frac{13}{14}a+\frac{104}{7} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{19}+a)(\frac{-19}{19}-p)& =(\color{red}{a}+\color{orange}{\frac{5}{19}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap-1a-\frac{5}{19}p-\frac{5}{19}.1& \text{Uitwerken } \\ & =-ap-1a-\frac{5}{19}p-\frac{5}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(10+q)(b+\frac{18}{18})& =(\color{red}{q}+\color{orange}{10}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(10)} . \color{green}{(b)} + \color{orange}{(10)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1q+10b+10.1& \text{Uitwerken } \\ & =bq+1q+10b+10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{3}{14}+a)(b+\frac{13}{12})& =(\color{red}{a}+\color{orange}{\frac{3}{14}}).(\color{green}{b}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{3}{14})} . \color{green}{(b)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{12}a+\frac{3}{14}b+\frac{3}{14}.\frac{13}{12}& \text{Uitwerken } \\ & =ab+\frac{13}{12}a+\frac{3}{14}b+\frac{39}{168} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{13}{12}a+\frac{3}{14}b+\frac{13}{56} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{14}{17})(p+\frac{1}{10})& =(\color{red}{p}+\color{orange}{\frac{14}{17}}).(\color{green}{p}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{14}{17})} . \color{green}{(p)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{10}p+\frac{14}{17}p+\frac{14}{17}.\frac{1}{10}& \text{Uitwerken } \\ & =p^2+(\frac{1}{10}+\frac{14}{17})p+\frac{14}{170} & \text{Neem samen} \\ &=p^2+\frac{157}{170}p+\frac{14}{170} & \text{Maak de som} \\ &=p^2+\frac{157}{170}p+\frac{7}{85} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{4}+x)(a+\frac{11}{7})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{7}x+1a+1.\frac{11}{7}& \text{Uitwerken } \\ & =ax+\frac{11}{7}x+1a+\frac{11}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{12}{12}-b)(\frac{-14}{6}+q)& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{7}{3}b+1q-1.\frac{7}{3}& \text{Uitwerken } \\ & =-bq+\frac{7}{3}b+1q-\frac{7}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-1}{14}-b)(q-\frac{-18}{9})& =(\color{red}{-b}+\color{orange}{\frac{-1}{14}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(2)} + \color{orange}{(\frac{-1}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bq-2b-\frac{1}{14}q-\frac{1}{14}.2& \text{Uitwerken } \\ & =-bq-2b-\frac{1}{14}q-\frac{2}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-2b-\frac{1}{14}q-\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{12}+a)(\frac{16}{14}-b)& =(\color{red}{a}+\color{orange}{\frac{-5}{6}}).(\color{green}{-b}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{8}{7}a+\frac{5}{6}b-\frac{5}{6}.\frac{8}{7}& \text{Uitwerken } \\ & =-ab+\frac{8}{7}a+\frac{5}{6}b-\frac{40}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{8}{7}a+\frac{5}{6}b-\frac{20}{21} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-12 19:12:34
Een site van Busleyden Atheneum Mechelen