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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-1}{4}-x)(a+\frac{13}{5})& =(\color{red}{-x}+\color{orange}{\frac{-1}{4}}).(\color{green}{a}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{13}{5}x-\frac{1}{4}a-\frac{1}{4}.\frac{13}{5}& \text{Uitwerken } \\ & =-ax-\frac{13}{5}x-\frac{1}{4}a-\frac{13}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{-10}{4})(\frac{18}{19}+a)& =(\color{red}{x}+\color{orange}{\frac{-5}{2}}).(\color{green}{a}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{18}{19}x-\frac{5}{2}a-\frac{5}{2}.\frac{18}{19}& \text{Uitwerken } \\ & =ax+\frac{18}{19}x-\frac{5}{2}a-\frac{90}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{18}{19}x-\frac{5}{2}a-\frac{45}{19} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{7}{4}-b)(a-\frac{18}{9})& =(\color{red}{-b}+\color{orange}{\frac{7}{4}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(-2)} + \color{orange}{(\frac{7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ab+2b+\frac{7}{4}a-\frac{7}{4}.2& \text{Uitwerken } \\ & =-ab+2b+\frac{7}{4}a-\frac{14}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+2b+\frac{7}{4}a-\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-19}{4})(\frac{9}{16}-x)& =(\color{red}{p}+\color{orange}{\frac{19}{4}}).(\color{green}{-x}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{19}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{9}{16}p-\frac{19}{4}x+\frac{19}{4}.\frac{9}{16}& \text{Uitwerken } \\ & =-px+\frac{9}{16}p-\frac{19}{4}x+\frac{171}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{-4}{5})((-17)-x)& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{-x}+\color{blue}{(-17)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(-17)} + \color{orange}{(\frac{4}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(-17)}& \text{Boogjes en uitschrijven} \\ & = -xx-17x-\frac{4}{5}x-\frac{4}{5}.17& \text{Uitwerken } \\ & =-x^2+((-17)+(\frac{-4}{5}))x-\frac{68}{5} & \text{Neem samen} \\ &=-x^2-\frac{89}{5}x-\frac{68}{5} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-14}{8})(b+\frac{-20}{19})& =(\color{red}{x}+\color{orange}{\frac{7}{4}}).(\color{green}{b}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{20}{19}x+\frac{7}{4}b-\frac{7}{4}.\frac{20}{19}& \text{Uitwerken } \\ & =bx-\frac{20}{19}x+\frac{7}{4}b-\frac{140}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{20}{19}x+\frac{7}{4}b-\frac{35}{19} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-8}{6}-q)(\frac{-10}{2}+a)& =(\color{red}{-q}+\color{orange}{\frac{-4}{3}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-5)} + \color{orange}{(\frac{-4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -aq+5q-\frac{4}{3}a+\frac{4}{3}.5& \text{Uitwerken } \\ & =-aq+5q-\frac{4}{3}a+\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{8}{10})(q-\frac{-17}{10})& =(\color{red}{a}+\color{orange}{\frac{-4}{5}}).(\color{green}{q}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{10}a-\frac{4}{5}q-\frac{4}{5}.\frac{17}{10}& \text{Uitwerken } \\ & =aq+\frac{17}{10}a-\frac{4}{5}q-\frac{68}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{17}{10}a-\frac{4}{5}q-\frac{34}{25} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-10}{6}+p)(\frac{1}{3}-a)& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{-a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{3}p+\frac{5}{3}a-\frac{5}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =-ap+\frac{1}{3}p+\frac{5}{3}a-\frac{5}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{11}{8}-q)(\frac{-20}{8}-a)& =(\color{red}{-q}+\color{orange}{\frac{11}{8}}).(\color{green}{-a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{11}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{2}q-\frac{11}{8}a-\frac{11}{8}.\frac{5}{2}& \text{Uitwerken } \\ & =aq+\frac{5}{2}q-\frac{11}{8}a-\frac{55}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-18}{9}+q)(p-\frac{6}{12})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{2}q-2p+2.\frac{1}{2}& \text{Uitwerken } \\ & =pq-\frac{1}{2}q-2p+\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{1}{2}q-2p+1 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-16}{11}+q)(b+\frac{9}{10})& =(\color{red}{q}+\color{orange}{\frac{-16}{11}}).(\color{green}{b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{10}q-\frac{16}{11}b-\frac{16}{11}.\frac{9}{10}& \text{Uitwerken } \\ & =bq+\frac{9}{10}q-\frac{16}{11}b-\frac{144}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{9}{10}q-\frac{16}{11}b-\frac{72}{55} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-16 10:43:33
Een site van Busleyden Atheneum Mechelen