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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{17}{4}-q)(\frac{2}{6}-p)& =(\color{red}{-q}+\color{orange}{\frac{17}{4}}).(\color{green}{-p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{17}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{3}q-\frac{17}{4}p+\frac{17}{4}.\frac{1}{3}& \text{Uitwerken } \\ & =pq-\frac{1}{3}q-\frac{17}{4}p+\frac{17}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{1}{8})(\frac{-17}{11}-q)& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{-q}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{17}{11}a-\frac{1}{8}q-\frac{1}{8}.\frac{17}{11}& \text{Uitwerken } \\ & =-aq-\frac{17}{11}a-\frac{1}{8}q-\frac{17}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-18}{20})(\frac{-15}{11}+a)& =(\color{red}{b}+\color{orange}{\frac{9}{10}}).(\color{green}{a}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{9}{10})} . \color{green}{(a)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{11}b+\frac{9}{10}a-\frac{9}{10}.\frac{15}{11}& \text{Uitwerken } \\ & =ab-\frac{15}{11}b+\frac{9}{10}a-\frac{135}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{15}{11}b+\frac{9}{10}a-\frac{27}{22} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p+\frac{18}{8})(\frac{-12}{20}+p)& =(\color{red}{p}+\color{orange}{\frac{9}{4}}).(\color{green}{p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{5}p+\frac{9}{4}p-\frac{9}{4}.\frac{3}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{5})+\frac{9}{4})p-(\frac{-27}{20}) & \text{Neem samen} \\ &=p^2+\frac{33}{20}p-(\frac{-27}{20}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(b+\frac{19}{18})(p-\frac{12}{17})& =(\color{red}{b}+\color{orange}{\frac{19}{18}}).(\color{green}{p}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{19}{18})} . \color{green}{(p)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{12}{17}b+\frac{19}{18}p-\frac{19}{18}.\frac{12}{17}& \text{Uitwerken } \\ & =bp-\frac{12}{17}b+\frac{19}{18}p-\frac{228}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{12}{17}b+\frac{19}{18}p-\frac{38}{51} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-18}{5}-q)(\frac{15}{6}+p)& =(\color{red}{-q}+\color{orange}{\frac{-18}{5}}).(\color{green}{p}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{2}q-\frac{18}{5}p-\frac{18}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =-pq-\frac{5}{2}q-\frac{18}{5}p-\frac{90}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{5}{2}q-\frac{18}{5}p-9 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x+\frac{-10}{5})(\frac{15}{2}-q)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{-q}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(-2)} . \color{green}{(-q)} + \color{orange}{(-2)} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{15}{2}x+2q-2.\frac{15}{2}& \text{Uitwerken } \\ & =-qx+\frac{15}{2}x+2q-\frac{30}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{15}{2}x+2q-15 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{16}+x)(b-\frac{-15}{3})& =(\color{red}{x}+\color{orange}{\frac{9}{8}}).(\color{green}{b}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(5)} + \color{orange}{(\frac{9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bx+5x+\frac{9}{8}b+\frac{9}{8}.5& \text{Uitwerken } \\ & =bx+5x+\frac{9}{8}b+\frac{45}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{7}+p)(a+\frac{4}{19})& =(\color{red}{p}+\color{orange}{\frac{5}{7}}).(\color{green}{a}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{19}p+\frac{5}{7}a+\frac{5}{7}.\frac{4}{19}& \text{Uitwerken } \\ & =ap+\frac{4}{19}p+\frac{5}{7}a+\frac{20}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-14}{7}+q)(\frac{-8}{14}-q)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{-q}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(-2)} . \color{green}{(-q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{4}{7}q+2q+2.\frac{4}{7}& \text{Uitwerken } \\ & =-q^2+((\frac{-4}{7})+2)q+(\frac{-8}{7}) & \text{Neem samen} \\ &=-q^2+\frac{10}{7}q+(\frac{-8}{7}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-14}{20})(\frac{-10}{17}-b)& =(\color{red}{b}+\color{orange}{\frac{-7}{10}}).(\color{green}{-b}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{10}{17}b+\frac{7}{10}b+\frac{7}{10}.\frac{10}{17}& \text{Uitwerken } \\ & =-b^2+((\frac{-10}{17})+\frac{7}{10})b+(\frac{-70}{170}) & \text{Neem samen} \\ &=-b^2+\frac{19}{170}b+(\frac{-70}{170}) & \text{Maak de som} \\ &=-b^2+\frac{19}{170}b+(\frac{-7}{17}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-16}{16})(a+\frac{-16}{19})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{16}{19}b-1a+1.\frac{16}{19}& \text{Uitwerken } \\ & =ab-\frac{16}{19}b-1a+\frac{16}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-04 23:28:53
Een site van Busleyden Atheneum Mechelen