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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{19}{8})(\frac{-10}{5}+x)& =(\color{red}{x}+\color{orange}{\frac{19}{8}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{19}{8})} . \color{green}{(x)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = xx-2x+\frac{19}{8}x-\frac{19}{8}.2& \text{Uitwerken } \\ & =x^2+((-2)+\frac{19}{8})x-(\frac{-38}{8}) & \text{Neem samen} \\ &=x^2+\frac{3}{8}x-(\frac{-38}{8}) & \text{Maak de som} \\ &=x^2+\frac{3}{8}x+\frac{19}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{4}-a)(x+\frac{18}{13})& =(\color{red}{-a}+\color{orange}{\frac{19}{4}}).(\color{green}{x}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{19}{4})} . \color{green}{(x)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{18}{13}a+\frac{19}{4}x+\frac{19}{4}.\frac{18}{13}& \text{Uitwerken } \\ & =-ax-\frac{18}{13}a+\frac{19}{4}x+\frac{342}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{18}{13}a+\frac{19}{4}x+\frac{171}{26} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{13}{16}-p)(b-\frac{5}{4})& =(\color{red}{-p}+\color{orange}{\frac{13}{16}}).(\color{green}{b}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{13}{16})} . \color{green}{(b)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{4}p+\frac{13}{16}b-\frac{13}{16}.\frac{5}{4}& \text{Uitwerken } \\ & =-bp+\frac{5}{4}p+\frac{13}{16}b-\frac{65}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-9}{2})(\frac{-11}{8}+x)& =(\color{red}{q}+\color{orange}{\frac{9}{2}}).(\color{green}{x}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{9}{2})} . \color{green}{(x)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{8}q+\frac{9}{2}x-\frac{9}{2}.\frac{11}{8}& \text{Uitwerken } \\ & =qx-\frac{11}{8}q+\frac{9}{2}x-\frac{99}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-2}{9})(a-\frac{14}{3})& =(\color{red}{q}+\color{orange}{\frac{-2}{9}}).(\color{green}{a}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{14}{3}q-\frac{2}{9}a+\frac{2}{9}.\frac{14}{3}& \text{Uitwerken } \\ & =aq-\frac{14}{3}q-\frac{2}{9}a+\frac{28}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-16}{12})(\frac{8}{9}+p)& =(\color{red}{a}+\color{orange}{\frac{4}{3}}).(\color{green}{p}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{9}a+\frac{4}{3}p+\frac{4}{3}.\frac{8}{9}& \text{Uitwerken } \\ & =ap+\frac{8}{9}a+\frac{4}{3}p+\frac{32}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-18}{18}+b)(q+\frac{19}{8})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{8}b-1q-1.\frac{19}{8}& \text{Uitwerken } \\ & =bq+\frac{19}{8}b-1q-\frac{19}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{17}{16}-x)((-6)-b)& =(\color{red}{-x}+\color{orange}{\frac{17}{16}}).(\color{green}{-b}+\color{blue}{(-6)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(-6)} + \color{orange}{(\frac{17}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = bx+6x-\frac{17}{16}b-\frac{17}{16}.6& \text{Uitwerken } \\ & =bx+6x-\frac{17}{16}b-\frac{102}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+6x-\frac{17}{16}b-\frac{51}{8} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{18}+a)(a-\frac{-17}{6})& =(\color{red}{a}+\color{orange}{\frac{-19}{18}}).(\color{green}{a}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{17}{6}a-\frac{19}{18}a-\frac{19}{18}.\frac{17}{6}& \text{Uitwerken } \\ & =a^2+(\frac{17}{6}+(\frac{-19}{18}))a-(\frac{-323}{108}) & \text{Neem samen} \\ &=a^2+\frac{32}{18}a-(\frac{-323}{108}) & \text{Maak de som} \\ &=a^2+\frac{16}{9}a+\frac{323}{108} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(\frac{-3}{12}-q)(\frac{5}{6}+b)& =(\color{red}{-q}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{6}q-\frac{1}{4}b-\frac{1}{4}.\frac{5}{6}& \text{Uitwerken } \\ & =-bq-\frac{5}{6}q-\frac{1}{4}b-\frac{5}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{11}{16}+b)(x-\frac{2}{13})& =(\color{red}{b}+\color{orange}{\frac{11}{16}}).(\color{green}{x}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{11}{16})} . \color{green}{(x)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{13}b+\frac{11}{16}x-\frac{11}{16}.\frac{2}{13}& \text{Uitwerken } \\ & =bx-\frac{2}{13}b+\frac{11}{16}x-\frac{22}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{2}{13}b+\frac{11}{16}x-\frac{11}{104} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{20}-q)(p-\frac{20}{16})& =(\color{red}{-q}+\color{orange}{\frac{-9}{10}}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{4}q-\frac{9}{10}p+\frac{9}{10}.\frac{5}{4}& \text{Uitwerken } \\ & =-pq+\frac{5}{4}q-\frac{9}{10}p+\frac{45}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{5}{4}q-\frac{9}{10}p+\frac{9}{8} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-12 08:53:41
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