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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{5}{20}-b)(\frac{10}{3}-x)& =(\color{red}{-b}+\color{orange}{\frac{1}{4}}).(\color{green}{-x}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{10}{3}b-\frac{1}{4}x+\frac{1}{4}.\frac{10}{3}& \text{Uitwerken } \\ & =bx-\frac{10}{3}b-\frac{1}{4}x+\frac{10}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{10}{3}b-\frac{1}{4}x+\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{9}{13})(a-\frac{-6}{15})& =(\color{red}{a}+\color{orange}{\frac{-9}{13}}).(\color{green}{a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{2}{5}a-\frac{9}{13}a-\frac{9}{13}.\frac{2}{5}& \text{Uitwerken } \\ & =a^2+(\frac{2}{5}+(\frac{-9}{13}))a-(\frac{-18}{65}) & \text{Neem samen} \\ &=a^2-\frac{19}{65}a-(\frac{-18}{65}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(a+\frac{3}{20})(b-1)& =(\color{red}{a}+\color{orange}{\frac{3}{20}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{3}{20})} . \color{green}{(b)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1a+\frac{3}{20}b-\frac{3}{20}.1& \text{Uitwerken } \\ & =ab-1a+\frac{3}{20}b-\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{10}{20}-p)(p+\frac{11}{7})& =(\color{red}{-p}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{11}{7}p+\frac{1}{2}p+\frac{1}{2}.\frac{11}{7}& \text{Uitwerken } \\ & =-p^2+((\frac{-11}{7})+\frac{1}{2})p+(\frac{-11}{14}) & \text{Neem samen} \\ &=-p^2-\frac{15}{14}p+(\frac{-11}{14}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{7}-x)(\frac{-12}{16}-q)& =(\color{red}{-x}+\color{orange}{\frac{-9}{7}}).(\color{green}{-q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{4}x+\frac{9}{7}q+\frac{9}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =qx+\frac{3}{4}x+\frac{9}{7}q+\frac{27}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-14}{4})(q+\frac{9}{13})& =(\color{red}{a}+\color{orange}{\frac{7}{2}}).(\color{green}{q}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{7}{2})} . \color{green}{(q)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{13}a+\frac{7}{2}q+\frac{7}{2}.\frac{9}{13}& \text{Uitwerken } \\ & =aq+\frac{9}{13}a+\frac{7}{2}q+\frac{63}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{14}{9}-x)(\frac{-20}{6}-b)& =(\color{red}{-x}+\color{orange}{\frac{14}{9}}).(\color{green}{-b}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{14}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{10}{3}x-\frac{14}{9}b-\frac{14}{9}.\frac{10}{3}& \text{Uitwerken } \\ & =bx+\frac{10}{3}x-\frac{14}{9}b-\frac{140}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(16-p)(\frac{-1}{13}-p)& =(\color{red}{-p}+\color{orange}{16}).(\color{green}{-p}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(16)} . \color{green}{(-p)} + \color{orange}{(16)} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{13}p-16p-16.\frac{1}{13}& \text{Uitwerken } \\ & =p^2+(\frac{1}{13}+(-16))p-(\frac{-16}{13}) & \text{Neem samen} \\ &=p^2-\frac{207}{13}p-(\frac{-16}{13}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{11}{10}-q)(\frac{16}{9}-a)& =(\color{red}{-q}+\color{orange}{\frac{11}{10}}).(\color{green}{-a}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(\frac{11}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{16}{9}q-\frac{11}{10}a+\frac{11}{10}.\frac{16}{9}& \text{Uitwerken } \\ & =aq-\frac{16}{9}q-\frac{11}{10}a+\frac{176}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{16}{9}q-\frac{11}{10}a+\frac{88}{45} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-9}{7}+q)(\frac{-3}{9}-q)& =(\color{red}{q}+\color{orange}{\frac{-9}{7}}).(\color{green}{-q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{3}q+\frac{9}{7}q+\frac{9}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{3})+\frac{9}{7})q+(\frac{-9}{21}) & \text{Neem samen} \\ &=-q^2+\frac{20}{21}q+(\frac{-9}{21}) & \text{Maak de som} \\ &=-q^2+\frac{20}{21}q+(\frac{-3}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(q-(-4))(a-\frac{-9}{18})& =(\color{red}{q}+\color{orange}{4}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{2}q+4a+4.\frac{1}{2}& \text{Uitwerken } \\ & =aq+\frac{1}{2}q+4a+\frac{4}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{1}{2}q+4a+2 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-3}{15})(\frac{6}{15}-b)& =(\color{red}{q}+\color{orange}{\frac{1}{5}}).(\color{green}{-b}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{5}q-\frac{1}{5}b+\frac{1}{5}.\frac{2}{5}& \text{Uitwerken } \\ & =-bq+\frac{2}{5}q-\frac{1}{5}b+\frac{2}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-05 22:47:06
Een site van Busleyden Atheneum Mechelen