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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{8}{6}+x)(a+\frac{9}{10})& =(\color{red}{x}+\color{orange}{\frac{4}{3}}).(\color{green}{a}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{10}x+\frac{4}{3}a+\frac{4}{3}.\frac{9}{10}& \text{Uitwerken } \\ & =ax+\frac{9}{10}x+\frac{4}{3}a+\frac{36}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{9}{10}x+\frac{4}{3}a+\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{3}{13})(\frac{-20}{13}-a)& =(\color{red}{a}+\color{orange}{\frac{-3}{13}}).(\color{green}{-a}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{20}{13}a+\frac{3}{13}a+\frac{3}{13}.\frac{20}{13}& \text{Uitwerken } \\ & =-a^2+((\frac{-20}{13})+\frac{3}{13})a+(\frac{-60}{169}) & \text{Neem samen} \\ &=-a^2-\frac{17}{13}a+(\frac{-60}{169}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-3}{2}+x)(\frac{-15}{11}-a)& =(\color{red}{x}+\color{orange}{\frac{-3}{2}}).(\color{green}{-a}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{15}{11}x+\frac{3}{2}a+\frac{3}{2}.\frac{15}{11}& \text{Uitwerken } \\ & =-ax-\frac{15}{11}x+\frac{3}{2}a+\frac{45}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{3}{13})(a-\frac{-16}{12})& =(\color{red}{x}+\color{orange}{\frac{-3}{13}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{3}x-\frac{3}{13}a-\frac{3}{13}.\frac{4}{3}& \text{Uitwerken } \\ & =ax+\frac{4}{3}x-\frac{3}{13}a-\frac{12}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{4}{3}x-\frac{3}{13}a-\frac{4}{13} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q-(-5))(\frac{9}{7}-p)& =(\color{red}{q}+\color{orange}{5}).(\color{green}{-p}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(5)} . \color{green}{(-p)} + \color{orange}{(5)} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{7}q-5p+5.\frac{9}{7}& \text{Uitwerken } \\ & =-pq+\frac{9}{7}q-5p+\frac{45}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{12}{5}-x)(a+\frac{-7}{15})& =(\color{red}{-x}+\color{orange}{\frac{12}{5}}).(\color{green}{a}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{12}{5})} . \color{green}{(a)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{15}x+\frac{12}{5}a-\frac{12}{5}.\frac{7}{15}& \text{Uitwerken } \\ & =-ax+\frac{7}{15}x+\frac{12}{5}a-\frac{84}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{7}{15}x+\frac{12}{5}a-\frac{28}{25} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{15}{10}-x)(b-\frac{-16}{10})& =(\color{red}{-x}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{8}{5}x+\frac{3}{2}b+\frac{3}{2}.\frac{8}{5}& \text{Uitwerken } \\ & =-bx-\frac{8}{5}x+\frac{3}{2}b+\frac{24}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{8}{5}x+\frac{3}{2}b+\frac{12}{5} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-10}{13})(\frac{3}{16}+a)& =(\color{red}{q}+\color{orange}{\frac{10}{13}}).(\color{green}{a}+\color{blue}{\frac{3}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{16})} + \color{orange}{(\frac{10}{13})} . \color{green}{(a)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{3}{16})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{16}q+\frac{10}{13}a+\frac{10}{13}.\frac{3}{16}& \text{Uitwerken } \\ & =aq+\frac{3}{16}q+\frac{10}{13}a+\frac{30}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{16}q+\frac{10}{13}a+\frac{15}{104} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-7}{6})(x-\frac{-20}{8})& =(\color{red}{b}+\color{orange}{\frac{7}{6}}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{7}{6})} . \color{green}{(x)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{2}b+\frac{7}{6}x+\frac{7}{6}.\frac{5}{2}& \text{Uitwerken } \\ & =bx+\frac{5}{2}b+\frac{7}{6}x+\frac{35}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{1}{4})(\frac{16}{14}+q)& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{q}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{8}{7}x+\frac{1}{4}q+\frac{1}{4}.\frac{8}{7}& \text{Uitwerken } \\ & =qx+\frac{8}{7}x+\frac{1}{4}q+\frac{8}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{8}{7}x+\frac{1}{4}q+\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{20}{6})(q+\frac{-1}{14})& =(\color{red}{x}+\color{orange}{\frac{10}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{10}{3})} . \color{green}{(q)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{14}x+\frac{10}{3}q-\frac{10}{3}.\frac{1}{14}& \text{Uitwerken } \\ & =qx-\frac{1}{14}x+\frac{10}{3}q-\frac{10}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{14}x+\frac{10}{3}q-\frac{5}{21} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b+\frac{6}{15})(b-\frac{-8}{4})& =(\color{red}{b}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bb+2b+\frac{2}{5}b+\frac{2}{5}.2& \text{Uitwerken } \\ & =b^2+(2+\frac{2}{5})b+\frac{4}{5} & \text{Neem samen} \\ &=b^2+\frac{12}{5}b+\frac{4}{5} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-20 21:19:21
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