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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-18}{5})(q-\frac{-15}{7})& =(\color{red}{x}+\color{orange}{\frac{18}{5}}).(\color{green}{q}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{18}{5})} . \color{green}{(q)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{15}{7}x+\frac{18}{5}q+\frac{18}{5}.\frac{15}{7}& \text{Uitwerken } \\ & =qx+\frac{15}{7}x+\frac{18}{5}q+\frac{270}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{15}{7}x+\frac{18}{5}q+\frac{54}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p-\frac{16}{4})(b+\frac{8}{8})& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(-4)} . \color{green}{(b)} + \color{orange}{(-4)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p-4b-4.1& \text{Uitwerken } \\ & =bp+1p-4b-4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-5}{10})(a+\frac{20}{10})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq+2q-\frac{1}{2}a-\frac{1}{2}.2& \text{Uitwerken } \\ & =aq+2q-\frac{1}{2}a-\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+2q-\frac{1}{2}a-1 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-\frac{4}{9})(x-\frac{17}{3})& =(\color{red}{q}+\color{orange}{\frac{-4}{9}}).(\color{green}{x}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{3}q-\frac{4}{9}x+\frac{4}{9}.\frac{17}{3}& \text{Uitwerken } \\ & =qx-\frac{17}{3}q-\frac{4}{9}x+\frac{68}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{6}+q)(\frac{-14}{17}-x)& =(\color{red}{q}+\color{orange}{\frac{5}{6}}).(\color{green}{-x}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{14}{17}q-\frac{5}{6}x-\frac{5}{6}.\frac{14}{17}& \text{Uitwerken } \\ & =-qx-\frac{14}{17}q-\frac{5}{6}x-\frac{70}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{14}{17}q-\frac{5}{6}x-\frac{35}{51} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-8}{8}-p)(p+\frac{-14}{19})& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{14}{19}p-1p+1.\frac{14}{19}& \text{Uitwerken } \\ & =-p^2+(\frac{14}{19}+(-1))p+(\frac{-14}{19}) & \text{Neem samen} \\ &=-p^2-\frac{5}{19}p+(\frac{-14}{19}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-4}{8})(18+q)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{18})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(18)} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = bq+18b+\frac{1}{2}q+\frac{1}{2}.18& \text{Uitwerken } \\ & =bq+18b+\frac{1}{2}q+\frac{18}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+18b+\frac{1}{2}q+9 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{17}{13}+b)(\frac{-16}{2}-p)& =(\color{red}{b}+\color{orange}{\frac{17}{13}}).(\color{green}{-p}+\color{blue}{(-8)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-8)} + \color{orange}{(\frac{17}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = -bp-8b-\frac{17}{13}p-\frac{17}{13}.8& \text{Uitwerken } \\ & =-bp-8b-\frac{17}{13}p-\frac{136}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{13}{20})(\frac{-13}{14}-q)& =(\color{red}{a}+\color{orange}{\frac{13}{20}}).(\color{green}{-q}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(\frac{13}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{13}{14}a-\frac{13}{20}q-\frac{13}{20}.\frac{13}{14}& \text{Uitwerken } \\ & =-aq-\frac{13}{14}a-\frac{13}{20}q-\frac{169}{280} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-14}{9}+q)(q-\frac{19}{5})& =(\color{red}{q}+\color{orange}{\frac{-14}{9}}).(\color{green}{q}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{19}{5}q-\frac{14}{9}q+\frac{14}{9}.\frac{19}{5}& \text{Uitwerken } \\ & =q^2+((\frac{-19}{5})+(\frac{-14}{9}))q+\frac{266}{45} & \text{Neem samen} \\ &=q^2-\frac{241}{45}q+\frac{266}{45} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{2}{20}-a)(\frac{-11}{10}+x)& =(\color{red}{-a}+\color{orange}{\frac{1}{10}}).(\color{green}{x}+\color{blue}{\frac{-11}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{10})} + \color{orange}{(\frac{1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-11}{10})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{11}{10}a+\frac{1}{10}x-\frac{1}{10}.\frac{11}{10}& \text{Uitwerken } \\ & =-ax+\frac{11}{10}a+\frac{1}{10}x-\frac{11}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-12}{3})(\frac{-19}{2}-a)& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{-a}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(-4)} . \color{green}{(-a)} + \color{orange}{(-4)} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{19}{2}p+4a+4.\frac{19}{2}& \text{Uitwerken } \\ & =-ap-\frac{19}{2}p+4a+\frac{76}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{19}{2}p+4a+38 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-15 02:28:47
Een site van Busleyden Atheneum Mechelen