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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{1}{3})(x-\frac{12}{8})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{2}x+\frac{1}{3}x-\frac{1}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{2})+\frac{1}{3})x-(\frac{-3}{6}) & \text{Neem samen} \\ &=x^2-\frac{7}{6}x-(\frac{-3}{6}) & \text{Maak de som} \\ &=x^2-\frac{7}{6}x+\frac{1}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(\frac{-6}{2}+x)(x+\frac{16}{17})& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{x}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(-3)} . \color{green}{(x)} + \color{orange}{(-3)} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{16}{17}x-3x-3.\frac{16}{17}& \text{Uitwerken } \\ & =x^2+(\frac{16}{17}+(-3))x-(\frac{-48}{17}) & \text{Neem samen} \\ &=x^2-\frac{35}{17}x-(\frac{-48}{17}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-11}{16})(\frac{-16}{14}-a)& =(\color{red}{x}+\color{orange}{\frac{-11}{16}}).(\color{green}{-a}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{8}{7}x+\frac{11}{16}a+\frac{11}{16}.\frac{8}{7}& \text{Uitwerken } \\ & =-ax-\frac{8}{7}x+\frac{11}{16}a+\frac{88}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{8}{7}x+\frac{11}{16}a+\frac{11}{14} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-15}{13})(x-\frac{19}{10})& =(\color{red}{x}+\color{orange}{\frac{-15}{13}}).(\color{green}{x}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{19}{10}x-\frac{15}{13}x+\frac{15}{13}.\frac{19}{10}& \text{Uitwerken } \\ & =x^2+((\frac{-19}{10})+(\frac{-15}{13}))x+\frac{285}{130} & \text{Neem samen} \\ &=x^2-\frac{397}{130}x+\frac{285}{130} & \text{Maak de som} \\ &=x^2-\frac{397}{130}x+\frac{57}{26} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(b-\frac{15}{10})(\frac{-19}{13}+p)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{13}b-\frac{3}{2}p+\frac{3}{2}.\frac{19}{13}& \text{Uitwerken } \\ & =bp-\frac{19}{13}b-\frac{3}{2}p+\frac{57}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{12}-x)(\frac{2}{15}-a)& =(\color{red}{-x}+\color{orange}{\frac{-3}{4}}).(\color{green}{-a}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{15}x+\frac{3}{4}a-\frac{3}{4}.\frac{2}{15}& \text{Uitwerken } \\ & =ax-\frac{2}{15}x+\frac{3}{4}a-\frac{6}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{2}{15}x+\frac{3}{4}a-\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{3}{11}+a)(\frac{-2}{7}-q)& =(\color{red}{a}+\color{orange}{\frac{3}{11}}).(\color{green}{-q}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{3}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{2}{7}a-\frac{3}{11}q-\frac{3}{11}.\frac{2}{7}& \text{Uitwerken } \\ & =-aq-\frac{2}{7}a-\frac{3}{11}q-\frac{6}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{2}{13})(x-\frac{-9}{8})& =(\color{red}{x}+\color{orange}{\frac{2}{13}}).(\color{green}{x}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{2}{13})} . \color{green}{(x)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{9}{8}x+\frac{2}{13}x+\frac{2}{13}.\frac{9}{8}& \text{Uitwerken } \\ & =x^2+(\frac{9}{8}+\frac{2}{13})x+\frac{18}{104} & \text{Neem samen} \\ &=x^2+\frac{133}{104}x+\frac{18}{104} & \text{Maak de som} \\ &=x^2+\frac{133}{104}x+\frac{9}{52} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-1}{15}+b)(\frac{5}{14}-a)& =(\color{red}{b}+\color{orange}{\frac{-1}{15}}).(\color{green}{-a}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{14}b+\frac{1}{15}a-\frac{1}{15}.\frac{5}{14}& \text{Uitwerken } \\ & =-ab+\frac{5}{14}b+\frac{1}{15}a-\frac{5}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{14}b+\frac{1}{15}a-\frac{1}{42} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-17}{8})(\frac{2}{2}-p)& =(\color{red}{p}+\color{orange}{\frac{-17}{8}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-17}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -pp+1p+\frac{17}{8}p-\frac{17}{8}.1& \text{Uitwerken } \\ & =-p^2+(1+\frac{17}{8})p-\frac{17}{8} & \text{Neem samen} \\ &=-p^2+\frac{25}{8}p-\frac{17}{8} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(x-\frac{17}{5})(\frac{-13}{20}-q)& =(\color{red}{x}+\color{orange}{\frac{-17}{5}}).(\color{green}{-q}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{20}x+\frac{17}{5}q+\frac{17}{5}.\frac{13}{20}& \text{Uitwerken } \\ & =-qx-\frac{13}{20}x+\frac{17}{5}q+\frac{221}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{2}{17}+q)(p+\frac{8}{7})& =(\color{red}{q}+\color{orange}{\frac{2}{17}}).(\color{green}{p}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{2}{17})} . \color{green}{(p)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{7}q+\frac{2}{17}p+\frac{2}{17}.\frac{8}{7}& \text{Uitwerken } \\ & =pq+\frac{8}{7}q+\frac{2}{17}p+\frac{16}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-07 11:12:05
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