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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{12}{19}+q)(\frac{-18}{19}-a)& =(\color{red}{q}+\color{orange}{\frac{12}{19}}).(\color{green}{-a}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{12}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{18}{19}q-\frac{12}{19}a-\frac{12}{19}.\frac{18}{19}& \text{Uitwerken } \\ & =-aq-\frac{18}{19}q-\frac{12}{19}a-\frac{216}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{3}{13}+x)(q-\frac{-2}{5})& =(\color{red}{x}+\color{orange}{\frac{3}{13}}).(\color{green}{q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{3}{13})} . \color{green}{(q)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{5}x+\frac{3}{13}q+\frac{3}{13}.\frac{2}{5}& \text{Uitwerken } \\ & =qx+\frac{2}{5}x+\frac{3}{13}q+\frac{6}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{18}{10}+b)(\frac{8}{17}+q)& =(\color{red}{b}+\color{orange}{\frac{9}{5}}).(\color{green}{q}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{9}{5})} . \color{green}{(q)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{8}{17}b+\frac{9}{5}q+\frac{9}{5}.\frac{8}{17}& \text{Uitwerken } \\ & =bq+\frac{8}{17}b+\frac{9}{5}q+\frac{72}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-16}{10})(\frac{10}{14}-a)& =(\color{red}{x}+\color{orange}{\frac{8}{5}}).(\color{green}{-a}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{8}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{7}x-\frac{8}{5}a+\frac{8}{5}.\frac{5}{7}& \text{Uitwerken } \\ & =-ax+\frac{5}{7}x-\frac{8}{5}a+\frac{40}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{5}{7}x-\frac{8}{5}a+\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{2}{9})(\frac{-7}{7}+q)& =(\color{red}{a}+\color{orange}{\frac{-2}{9}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a-\frac{2}{9}q+\frac{2}{9}.1& \text{Uitwerken } \\ & =aq-1a-\frac{2}{9}q+\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{3}{8}+x)(\frac{-16}{5}+x)& =(\color{red}{x}+\color{orange}{\frac{3}{8}}).(\color{green}{x}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{3}{8})} . \color{green}{(x)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{16}{5}x+\frac{3}{8}x-\frac{3}{8}.\frac{16}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-16}{5})+\frac{3}{8})x-(\frac{-48}{40}) & \text{Neem samen} \\ &=x^2-\frac{113}{40}x-(\frac{-48}{40}) & \text{Maak de som} \\ &=x^2-\frac{113}{40}x+\frac{6}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{-17}{11}-p)(a+\frac{-11}{3})& =(\color{red}{-p}+\color{orange}{\frac{-17}{11}}).(\color{green}{a}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{-17}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{11}{3}p-\frac{17}{11}a+\frac{17}{11}.\frac{11}{3}& \text{Uitwerken } \\ & =-ap+\frac{11}{3}p-\frac{17}{11}a+\frac{187}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{11}{3}p-\frac{17}{11}a+\frac{17}{3} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{9}{11}+a)(\frac{-10}{11}-x)& =(\color{red}{a}+\color{orange}{\frac{9}{11}}).(\color{green}{-x}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{9}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{10}{11}a-\frac{9}{11}x-\frac{9}{11}.\frac{10}{11}& \text{Uitwerken } \\ & =-ax-\frac{10}{11}a-\frac{9}{11}x-\frac{90}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-2}{19}+b)(a+\frac{17}{9})& =(\color{red}{b}+\color{orange}{\frac{-2}{19}}).(\color{green}{a}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{-2}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{9}b-\frac{2}{19}a-\frac{2}{19}.\frac{17}{9}& \text{Uitwerken } \\ & =ab+\frac{17}{9}b-\frac{2}{19}a-\frac{34}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-13}{10}-a)(q-\frac{10}{20})& =(\color{red}{-a}+\color{orange}{\frac{-13}{10}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{2}a-\frac{13}{10}q+\frac{13}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =-aq+\frac{1}{2}a-\frac{13}{10}q+\frac{13}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{7}-p)(x-\frac{-12}{13})& =(\color{red}{-p}+\color{orange}{\frac{10}{7}}).(\color{green}{x}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{12}{13}p+\frac{10}{7}x+\frac{10}{7}.\frac{12}{13}& \text{Uitwerken } \\ & =-px-\frac{12}{13}p+\frac{10}{7}x+\frac{120}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-3}{11}+a)(p+\frac{14}{3})& =(\color{red}{a}+\color{orange}{\frac{-3}{11}}).(\color{green}{p}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{14}{3}a-\frac{3}{11}p-\frac{3}{11}.\frac{14}{3}& \text{Uitwerken } \\ & =ap+\frac{14}{3}a-\frac{3}{11}p-\frac{42}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{14}{3}a-\frac{3}{11}p-\frac{14}{11} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-13 16:32:52
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