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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-9}{10}+x)(\frac{-9}{14}-p)& =(\color{red}{x}+\color{orange}{\frac{-9}{10}}).(\color{green}{-p}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{9}{14}x+\frac{9}{10}p+\frac{9}{10}.\frac{9}{14}& \text{Uitwerken } \\ & =-px-\frac{9}{14}x+\frac{9}{10}p+\frac{81}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-11}{11}+x)(\frac{-13}{19}-x)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{13}{19}x+1x+1.\frac{13}{19}& \text{Uitwerken } \\ & =-x^2+((\frac{-13}{19})+1)x+(\frac{-13}{19}) & \text{Neem samen} \\ &=-x^2+\frac{6}{19}x+(\frac{-13}{19}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-15}{17}-p)(\frac{-19}{15}+q)& =(\color{red}{-p}+\color{orange}{\frac{-15}{17}}).(\color{green}{q}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-15}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{19}{15}p-\frac{15}{17}q+\frac{15}{17}.\frac{19}{15}& \text{Uitwerken } \\ & =-pq+\frac{19}{15}p-\frac{15}{17}q+\frac{285}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{19}{15}p-\frac{15}{17}q+\frac{19}{17} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{17}{3}+b)(\frac{12}{18}+q)& =(\color{red}{b}+\color{orange}{\frac{17}{3}}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{17}{3})} . \color{green}{(q)} + \color{orange}{(\frac{17}{3})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{3}b+\frac{17}{3}q+\frac{17}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =bq+\frac{2}{3}b+\frac{17}{3}q+\frac{34}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{18}{2}-b)(\frac{8}{3}+q)& =(\color{red}{-b}+\color{orange}{9}).(\color{green}{q}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(9)} . \color{green}{(q)} + \color{orange}{(9)} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{8}{3}b+9q+9.\frac{8}{3}& \text{Uitwerken } \\ & =-bq-\frac{8}{3}b+9q+\frac{72}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{8}{3}b+9q+24 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{4}{13}+x)(a+\frac{1}{4})& =(\color{red}{x}+\color{orange}{\frac{4}{13}}).(\color{green}{a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{4}{13})} . \color{green}{(a)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{4}x+\frac{4}{13}a+\frac{4}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =ax+\frac{1}{4}x+\frac{4}{13}a+\frac{4}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{4}x+\frac{4}{13}a+\frac{1}{13} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{4}{20}+b)(\frac{11}{4}-p)& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{-p}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{11}{4}b-\frac{1}{5}p+\frac{1}{5}.\frac{11}{4}& \text{Uitwerken } \\ & =-bp+\frac{11}{4}b-\frac{1}{5}p+\frac{11}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-8}{4}-x)(x+\frac{-6}{16})& =(\color{red}{-x}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{3}{8}x-2x+2.\frac{3}{8}& \text{Uitwerken } \\ & =-x^2+(\frac{3}{8}+(-2))x+(\frac{-6}{8}) & \text{Neem samen} \\ &=-x^2-\frac{13}{8}x+(\frac{-6}{8}) & \text{Maak de som} \\ &=-x^2-\frac{13}{8}x+(\frac{-3}{4}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(p-\frac{4}{7})(\frac{-13}{14}+a)& =(\color{red}{p}+\color{orange}{\frac{-4}{7}}).(\color{green}{a}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{14}p-\frac{4}{7}a+\frac{4}{7}.\frac{13}{14}& \text{Uitwerken } \\ & =ap-\frac{13}{14}p-\frac{4}{7}a+\frac{52}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{13}{14}p-\frac{4}{7}a+\frac{26}{49} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-15}{4}+b)(b+\frac{12}{16})& =(\color{red}{b}+\color{orange}{\frac{-15}{4}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{4}b-\frac{15}{4}b-\frac{15}{4}.\frac{3}{4}& \text{Uitwerken } \\ & =b^2+(\frac{3}{4}+(\frac{-15}{4}))b-(\frac{-45}{16}) & \text{Neem samen} \\ &=b^2-\frac{12}{4}b-(\frac{-45}{16}) & \text{Maak de som} \\ &=b^2-3b+\frac{45}{16} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{5}-a)(b-\frac{-17}{20})& =(\color{red}{-a}+\color{orange}{\frac{16}{5}}).(\color{green}{b}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{16}{5})} . \color{green}{(b)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{17}{20}a+\frac{16}{5}b+\frac{16}{5}.\frac{17}{20}& \text{Uitwerken } \\ & =-ab-\frac{17}{20}a+\frac{16}{5}b+\frac{272}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{17}{20}a+\frac{16}{5}b+\frac{68}{25} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-17}{3}-x)(\frac{-12}{15}-q)& =(\color{red}{-x}+\color{orange}{\frac{-17}{3}}).(\color{green}{-q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{5}x+\frac{17}{3}q+\frac{17}{3}.\frac{4}{5}& \text{Uitwerken } \\ & =qx+\frac{4}{5}x+\frac{17}{3}q+\frac{68}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-24 02:55:35
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