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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-5}{16}-x)(\frac{-19}{19}+q)& =(\color{red}{-x}+\color{orange}{\frac{-5}{16}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-5}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1x-\frac{5}{16}q+\frac{5}{16}.1& \text{Uitwerken } \\ & =-qx+1x-\frac{5}{16}q+\frac{5}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-10}{9}+p)(\frac{16}{10}+q)& =(\color{red}{p}+\color{orange}{\frac{-10}{9}}).(\color{green}{q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{5}p-\frac{10}{9}q-\frac{10}{9}.\frac{8}{5}& \text{Uitwerken } \\ & =pq+\frac{8}{5}p-\frac{10}{9}q-\frac{80}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{8}{5}p-\frac{10}{9}q-\frac{16}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{17}{20}+p)(\frac{-18}{11}+b)& =(\color{red}{p}+\color{orange}{\frac{17}{20}}).(\color{green}{b}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{17}{20})} . \color{green}{(b)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{18}{11}p+\frac{17}{20}b-\frac{17}{20}.\frac{18}{11}& \text{Uitwerken } \\ & =bp-\frac{18}{11}p+\frac{17}{20}b-\frac{306}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{18}{11}p+\frac{17}{20}b-\frac{153}{110} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{6}{2}-p)(\frac{17}{4}+a)& =(\color{red}{-p}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{4}p+3a+3.\frac{17}{4}& \text{Uitwerken } \\ & =-ap-\frac{17}{4}p+3a+\frac{51}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{20}-q)(b-\frac{-18}{19})& =(\color{red}{-q}+\color{orange}{\frac{-9}{20}}).(\color{green}{b}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{18}{19}q-\frac{9}{20}b-\frac{9}{20}.\frac{18}{19}& \text{Uitwerken } \\ & =-bq-\frac{18}{19}q-\frac{9}{20}b-\frac{162}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{18}{19}q-\frac{9}{20}b-\frac{81}{190} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-14}{11}-x)(\frac{-17}{5}+p)& =(\color{red}{-x}+\color{orange}{\frac{-14}{11}}).(\color{green}{p}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{17}{5}x-\frac{14}{11}p+\frac{14}{11}.\frac{17}{5}& \text{Uitwerken } \\ & =-px+\frac{17}{5}x-\frac{14}{11}p+\frac{238}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-17}{9}+p)(\frac{13}{5}+a)& =(\color{red}{p}+\color{orange}{\frac{-17}{9}}).(\color{green}{a}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{5}p-\frac{17}{9}a-\frac{17}{9}.\frac{13}{5}& \text{Uitwerken } \\ & =ap+\frac{13}{5}p-\frac{17}{9}a-\frac{221}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-13}{7})(q+\frac{6}{17})& =(\color{red}{a}+\color{orange}{\frac{13}{7}}).(\color{green}{q}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{13}{7})} . \color{green}{(q)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{17}a+\frac{13}{7}q+\frac{13}{7}.\frac{6}{17}& \text{Uitwerken } \\ & =aq+\frac{6}{17}a+\frac{13}{7}q+\frac{78}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{16}{13}-a)(\frac{-11}{20}+b)& =(\color{red}{-a}+\color{orange}{\frac{16}{13}}).(\color{green}{b}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{16}{13})} . \color{green}{(b)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{11}{20}a+\frac{16}{13}b-\frac{16}{13}.\frac{11}{20}& \text{Uitwerken } \\ & =-ab+\frac{11}{20}a+\frac{16}{13}b-\frac{176}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{11}{20}a+\frac{16}{13}b-\frac{44}{65} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-10}{7})(\frac{4}{8}-a)& =(\color{red}{a}+\color{orange}{\frac{-10}{7}}).(\color{green}{-a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{2}a+\frac{10}{7}a-\frac{10}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{2}+\frac{10}{7})a-\frac{10}{14} & \text{Neem samen} \\ &=-a^2+\frac{27}{14}a-\frac{10}{14} & \text{Maak de som} \\ &=-a^2+\frac{27}{14}a-\frac{5}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{2}+b)(\frac{9}{11}+p)& =(\color{red}{b}+\color{orange}{\frac{-13}{2}}).(\color{green}{p}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{11}b-\frac{13}{2}p-\frac{13}{2}.\frac{9}{11}& \text{Uitwerken } \\ & =bp+\frac{9}{11}b-\frac{13}{2}p-\frac{117}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{11}{17})(\frac{1}{18}-x)& =(\color{red}{a}+\color{orange}{\frac{-11}{17}}).(\color{green}{-x}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{-11}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{18}a+\frac{11}{17}x-\frac{11}{17}.\frac{1}{18}& \text{Uitwerken } \\ & =-ax+\frac{1}{18}a+\frac{11}{17}x-\frac{11}{306} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-23 13:37:02
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