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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-6}{9})(\frac{-1}{6}-p)& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{-p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{6}p-\frac{2}{3}p-\frac{2}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{6})+(\frac{-2}{3}))p-\frac{2}{18} & \text{Neem samen} \\ &=-p^2-\frac{5}{6}p-\frac{2}{18} & \text{Maak de som} \\ &=-p^2-\frac{5}{6}p-\frac{1}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-8}{7}+q)(\frac{15}{11}+a)& =(\color{red}{q}+\color{orange}{\frac{-8}{7}}).(\color{green}{a}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{15}{11}q-\frac{8}{7}a-\frac{8}{7}.\frac{15}{11}& \text{Uitwerken } \\ & =aq+\frac{15}{11}q-\frac{8}{7}a-\frac{120}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{18}{20})(q-(-19))& =(\color{red}{a}+\color{orange}{\frac{9}{10}}).(\color{green}{q}+\color{blue}{19})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(19)} + \color{orange}{(\frac{9}{10})} . \color{green}{(q)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = aq+19a+\frac{9}{10}q+\frac{9}{10}.19& \text{Uitwerken } \\ & =aq+19a+\frac{9}{10}q+\frac{171}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-19}{12})(\frac{15}{17}-a)& =(\color{red}{q}+\color{orange}{\frac{19}{12}}).(\color{green}{-a}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{19}{12})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{15}{17}q-\frac{19}{12}a+\frac{19}{12}.\frac{15}{17}& \text{Uitwerken } \\ & =-aq+\frac{15}{17}q-\frac{19}{12}a+\frac{285}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{15}{17}q-\frac{19}{12}a+\frac{95}{68} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-5}{7}-x)(b+\frac{-15}{19})& =(\color{red}{-x}+\color{orange}{\frac{-5}{7}}).(\color{green}{b}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{15}{19}x-\frac{5}{7}b+\frac{5}{7}.\frac{15}{19}& \text{Uitwerken } \\ & =-bx+\frac{15}{19}x-\frac{5}{7}b+\frac{75}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{9}{7}-q)(\frac{8}{4}+p)& =(\color{red}{-q}+\color{orange}{\frac{9}{7}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{9}{7})} . \color{green}{(p)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -pq-2q+\frac{9}{7}p+\frac{9}{7}.2& \text{Uitwerken } \\ & =-pq-2q+\frac{9}{7}p+\frac{18}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-16}{9})(\frac{-1}{17}+b)& =(\color{red}{p}+\color{orange}{\frac{16}{9}}).(\color{green}{b}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{16}{9})} . \color{green}{(b)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{17}p+\frac{16}{9}b-\frac{16}{9}.\frac{1}{17}& \text{Uitwerken } \\ & =bp-\frac{1}{17}p+\frac{16}{9}b-\frac{16}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-17}{14})(x-\frac{-16}{7})& =(\color{red}{p}+\color{orange}{\frac{17}{14}}).(\color{green}{x}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{17}{14})} . \color{green}{(x)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{16}{7}p+\frac{17}{14}x+\frac{17}{14}.\frac{16}{7}& \text{Uitwerken } \\ & =px+\frac{16}{7}p+\frac{17}{14}x+\frac{272}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{16}{7}p+\frac{17}{14}x+\frac{136}{49} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-6}{16}-p)(\frac{19}{2}-a)& =(\color{red}{-p}+\color{orange}{\frac{-3}{8}}).(\color{green}{-a}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{2}p+\frac{3}{8}a-\frac{3}{8}.\frac{19}{2}& \text{Uitwerken } \\ & =ap-\frac{19}{2}p+\frac{3}{8}a-\frac{57}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{6}{15}+b)(q+\frac{-20}{19})& =(\color{red}{b}+\color{orange}{\frac{2}{5}}).(\color{green}{q}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{20}{19}b+\frac{2}{5}q-\frac{2}{5}.\frac{20}{19}& \text{Uitwerken } \\ & =bq-\frac{20}{19}b+\frac{2}{5}q-\frac{40}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{20}{19}b+\frac{2}{5}q-\frac{8}{19} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-3}{15}+b)(p+\frac{-8}{7})& =(\color{red}{b}+\color{orange}{\frac{-1}{5}}).(\color{green}{p}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{7}b-\frac{1}{5}p+\frac{1}{5}.\frac{8}{7}& \text{Uitwerken } \\ & =bp-\frac{8}{7}b-\frac{1}{5}p+\frac{8}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{7}{4}+p)(q-\frac{19}{18})& =(\color{red}{p}+\color{orange}{\frac{7}{4}}).(\color{green}{q}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{18}p+\frac{7}{4}q-\frac{7}{4}.\frac{19}{18}& \text{Uitwerken } \\ & =pq-\frac{19}{18}p+\frac{7}{4}q-\frac{133}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-27 06:40:38
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