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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{17}-x)(x-\frac{10}{12})& =(\color{red}{-x}+\color{orange}{\frac{20}{17}}).(\color{green}{x}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{20}{17})} . \color{green}{(x)} + \color{orange}{(\frac{20}{17})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{5}{6}x+\frac{20}{17}x-\frac{20}{17}.\frac{5}{6}& \text{Uitwerken } \\ & =-x^2+(\frac{5}{6}+\frac{20}{17})x-\frac{100}{102} & \text{Neem samen} \\ &=-x^2+\frac{205}{102}x-\frac{100}{102} & \text{Maak de som} \\ &=-x^2+\frac{205}{102}x-\frac{50}{51} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{13}{20}+q)(\frac{4}{16}-b)& =(\color{red}{q}+\color{orange}{\frac{13}{20}}).(\color{green}{-b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{13}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{4}q-\frac{13}{20}b+\frac{13}{20}.\frac{1}{4}& \text{Uitwerken } \\ & =-bq+\frac{1}{4}q-\frac{13}{20}b+\frac{13}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{4}{9}+x)(a+\frac{-5}{16})& =(\color{red}{x}+\color{orange}{\frac{4}{9}}).(\color{green}{a}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{16}x+\frac{4}{9}a-\frac{4}{9}.\frac{5}{16}& \text{Uitwerken } \\ & =ax-\frac{5}{16}x+\frac{4}{9}a-\frac{20}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{16}x+\frac{4}{9}a-\frac{5}{36} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-19}{11})(q+\frac{-16}{10})& =(\color{red}{b}+\color{orange}{\frac{-19}{11}}).(\color{green}{q}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{5}b-\frac{19}{11}q+\frac{19}{11}.\frac{8}{5}& \text{Uitwerken } \\ & =bq-\frac{8}{5}b-\frac{19}{11}q+\frac{152}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-4}{10})(p-\frac{17}{10})& =(\color{red}{a}+\color{orange}{\frac{-2}{5}}).(\color{green}{p}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{17}{10}a-\frac{2}{5}p+\frac{2}{5}.\frac{17}{10}& \text{Uitwerken } \\ & =ap-\frac{17}{10}a-\frac{2}{5}p+\frac{34}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{17}{10}a-\frac{2}{5}p+\frac{17}{25} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x-\frac{17}{14})(a+\frac{-1}{4})& =(\color{red}{x}+\color{orange}{\frac{-17}{14}}).(\color{green}{a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{4}x-\frac{17}{14}a+\frac{17}{14}.\frac{1}{4}& \text{Uitwerken } \\ & =ax-\frac{1}{4}x-\frac{17}{14}a+\frac{17}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{4}{19}+q)(\frac{7}{2}-q)& =(\color{red}{q}+\color{orange}{\frac{4}{19}}).(\color{green}{-q}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{4}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{7}{2}q-\frac{4}{19}q+\frac{4}{19}.\frac{7}{2}& \text{Uitwerken } \\ & =-q^2+(\frac{7}{2}+(\frac{-4}{19}))q+(\frac{-28}{38}) & \text{Neem samen} \\ &=-q^2+\frac{125}{38}q+(\frac{-28}{38}) & \text{Maak de som} \\ &=-q^2+\frac{125}{38}q+(\frac{-14}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-18}{16}+p)(\frac{-8}{4}-q)& =(\color{red}{p}+\color{orange}{\frac{-9}{8}}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-9}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -pq-2p+\frac{9}{8}q+\frac{9}{8}.2& \text{Uitwerken } \\ & =-pq-2p+\frac{9}{8}q+\frac{18}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-2p+\frac{9}{8}q+\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b+\frac{7}{10})(a+\frac{1}{20})& =(\color{red}{b}+\color{orange}{\frac{7}{10}}).(\color{green}{a}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{20}b+\frac{7}{10}a+\frac{7}{10}.\frac{1}{20}& \text{Uitwerken } \\ & =ab+\frac{1}{20}b+\frac{7}{10}a+\frac{7}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{12}{14}+x)(a-\frac{-9}{6})& =(\color{red}{x}+\color{orange}{\frac{6}{7}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{6}{7})} . \color{green}{(a)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{2}x+\frac{6}{7}a+\frac{6}{7}.\frac{3}{2}& \text{Uitwerken } \\ & =ax+\frac{3}{2}x+\frac{6}{7}a+\frac{18}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{2}x+\frac{6}{7}a+\frac{9}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-9}{18}+q)(p+\frac{20}{16})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{4}q-\frac{1}{2}p-\frac{1}{2}.\frac{5}{4}& \text{Uitwerken } \\ & =pq+\frac{5}{4}q-\frac{1}{2}p-\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{1}{4}+p)(\frac{3}{2}-b)& =(\color{red}{p}+\color{orange}{\frac{1}{4}}).(\color{green}{-b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{3}{2}p-\frac{1}{4}b+\frac{1}{4}.\frac{3}{2}& \text{Uitwerken } \\ & =-bp+\frac{3}{2}p-\frac{1}{4}b+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-25 09:16:57
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