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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-18}{14})(q+\frac{4}{9})& =(\color{red}{p}+\color{orange}{\frac{9}{7}}).(\color{green}{q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{9}{7})} . \color{green}{(q)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{9}p+\frac{9}{7}q+\frac{9}{7}.\frac{4}{9}& \text{Uitwerken } \\ & =pq+\frac{4}{9}p+\frac{9}{7}q+\frac{36}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{4}{9}p+\frac{9}{7}q+\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{7}{8}-x)(q-\frac{10}{13})& =(\color{red}{-x}+\color{orange}{\frac{7}{8}}).(\color{green}{q}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{10}{13}x+\frac{7}{8}q-\frac{7}{8}.\frac{10}{13}& \text{Uitwerken } \\ & =-qx+\frac{10}{13}x+\frac{7}{8}q-\frac{70}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{10}{13}x+\frac{7}{8}q-\frac{35}{52} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q-\frac{16}{10})(\frac{-9}{15}+b)& =(\color{red}{q}+\color{orange}{\frac{-8}{5}}).(\color{green}{b}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{5}q-\frac{8}{5}b+\frac{8}{5}.\frac{3}{5}& \text{Uitwerken } \\ & =bq-\frac{3}{5}q-\frac{8}{5}b+\frac{24}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{19}{11}+q)(q+\frac{-6}{5})& =(\color{red}{q}+\color{orange}{\frac{19}{11}}).(\color{green}{q}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{19}{11})} . \color{green}{(q)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{6}{5}q+\frac{19}{11}q-\frac{19}{11}.\frac{6}{5}& \text{Uitwerken } \\ & =q^2+((\frac{-6}{5})+\frac{19}{11})q-(\frac{-114}{55}) & \text{Neem samen} \\ &=q^2+\frac{29}{55}q-(\frac{-114}{55}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{15}-q)(\frac{-1}{15}+p)& =(\color{red}{-q}+\color{orange}{\frac{-3}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{15}q-\frac{3}{5}p+\frac{3}{5}.\frac{1}{15}& \text{Uitwerken } \\ & =-pq+\frac{1}{15}q-\frac{3}{5}p+\frac{3}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{1}{15}q-\frac{3}{5}p+\frac{1}{25} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-16}{11}+a)(b+\frac{16}{10})& =(\color{red}{a}+\color{orange}{\frac{-16}{11}}).(\color{green}{b}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{5}a-\frac{16}{11}b-\frac{16}{11}.\frac{8}{5}& \text{Uitwerken } \\ & =ab+\frac{8}{5}a-\frac{16}{11}b-\frac{128}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{11}-b)(\frac{-18}{10}-q)& =(\color{red}{-b}+\color{orange}{\frac{13}{11}}).(\color{green}{-q}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{13}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{5}b-\frac{13}{11}q-\frac{13}{11}.\frac{9}{5}& \text{Uitwerken } \\ & =bq+\frac{9}{5}b-\frac{13}{11}q-\frac{117}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-10}{9})(\frac{16}{8}-b)& =(\color{red}{p}+\color{orange}{\frac{-10}{9}}).(\color{green}{-b}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bp+2p+\frac{10}{9}b-\frac{10}{9}.2& \text{Uitwerken } \\ & =-bp+2p+\frac{10}{9}b-\frac{20}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-3}{17}-a)(\frac{5}{13}+q)& =(\color{red}{-a}+\color{orange}{\frac{-3}{17}}).(\color{green}{q}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-3}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{13}a-\frac{3}{17}q-\frac{3}{17}.\frac{5}{13}& \text{Uitwerken } \\ & =-aq-\frac{5}{13}a-\frac{3}{17}q-\frac{15}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-20}{2})(p-\frac{-14}{6})& =(\color{red}{a}+\color{orange}{(-10)}).(\color{green}{p}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(-10)} . \color{green}{(p)} + \color{orange}{(-10)} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{3}a-10p-10.\frac{7}{3}& \text{Uitwerken } \\ & =ap+\frac{7}{3}a-10p-\frac{70}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{19}{9})(\frac{6}{17}-q)& =(\color{red}{b}+\color{orange}{\frac{19}{9}}).(\color{green}{-q}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{19}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{6}{17}b-\frac{19}{9}q+\frac{19}{9}.\frac{6}{17}& \text{Uitwerken } \\ & =-bq+\frac{6}{17}b-\frac{19}{9}q+\frac{114}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{6}{17}b-\frac{19}{9}q+\frac{38}{51} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-5}{20}-p)(q-\frac{15}{18})& =(\color{red}{-p}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{6}p-\frac{1}{4}q+\frac{1}{4}.\frac{5}{6}& \text{Uitwerken } \\ & =-pq+\frac{5}{6}p-\frac{1}{4}q+\frac{5}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-15 15:56:13
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