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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{3}{4}+a)(\frac{4}{8}-x)& =(\color{red}{a}+\color{orange}{\frac{3}{4}}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{2}a-\frac{3}{4}x+\frac{3}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =-ax+\frac{1}{2}a-\frac{3}{4}x+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{16}{10})(\frac{5}{8}-q)& =(\color{red}{a}+\color{orange}{\frac{8}{5}}).(\color{green}{-q}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{8}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{8}a-\frac{8}{5}q+\frac{8}{5}.\frac{5}{8}& \text{Uitwerken } \\ & =-aq+\frac{5}{8}a-\frac{8}{5}q+\frac{40}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{5}{8}a-\frac{8}{5}q+1 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-14}{6})(\frac{-14}{9}+a)& =(\color{red}{q}+\color{orange}{\frac{-7}{3}}).(\color{green}{a}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{14}{9}q-\frac{7}{3}a+\frac{7}{3}.\frac{14}{9}& \text{Uitwerken } \\ & =aq-\frac{14}{9}q-\frac{7}{3}a+\frac{98}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{15}{4})(a-\frac{15}{6})& =(\color{red}{x}+\color{orange}{\frac{-15}{4}}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{2}x-\frac{15}{4}a+\frac{15}{4}.\frac{5}{2}& \text{Uitwerken } \\ & =ax-\frac{5}{2}x-\frac{15}{4}a+\frac{75}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-11}{4})(\frac{-5}{20}+q)& =(\color{red}{q}+\color{orange}{\frac{-11}{4}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-11}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{4})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{4}q-\frac{11}{4}q+\frac{11}{4}.\frac{1}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{4})+(\frac{-11}{4}))q+\frac{11}{16} & \text{Neem samen} \\ &=q^2-\frac{12}{4}q+\frac{11}{16} & \text{Maak de som} \\ &=q^2-3q+\frac{11}{16} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-11}{2})(\frac{-19}{18}-q)& =(\color{red}{p}+\color{orange}{\frac{11}{2}}).(\color{green}{-q}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{11}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{18}p-\frac{11}{2}q-\frac{11}{2}.\frac{19}{18}& \text{Uitwerken } \\ & =-pq-\frac{19}{18}p-\frac{11}{2}q-\frac{209}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{8}+q)(\frac{2}{4}+a)& =(\color{red}{q}+\color{orange}{\frac{13}{8}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{13}{8})} . \color{green}{(a)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{2}q+\frac{13}{8}a+\frac{13}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =aq+\frac{1}{2}q+\frac{13}{8}a+\frac{13}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{2}{13})(\frac{-13}{14}+x)& =(\color{red}{a}+\color{orange}{\frac{-2}{13}}).(\color{green}{x}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{14}a-\frac{2}{13}x+\frac{2}{13}.\frac{13}{14}& \text{Uitwerken } \\ & =ax-\frac{13}{14}a-\frac{2}{13}x+\frac{26}{182} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{13}{14}a-\frac{2}{13}x+\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-9}{12}-a)(\frac{7}{11}-q)& =(\color{red}{-a}+\color{orange}{\frac{-3}{4}}).(\color{green}{-q}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{11}a+\frac{3}{4}q-\frac{3}{4}.\frac{7}{11}& \text{Uitwerken } \\ & =aq-\frac{7}{11}a+\frac{3}{4}q-\frac{21}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{2}{9})(\frac{-14}{14}+p)& =(\color{red}{p}+\color{orange}{\frac{-2}{9}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pp-1p-\frac{2}{9}p+\frac{2}{9}.1& \text{Uitwerken } \\ & =p^2+((-1)+(\frac{-2}{9}))p+\frac{2}{9} & \text{Neem samen} \\ &=p^2-\frac{11}{9}p+\frac{2}{9} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{10}-b)(p-\frac{9}{16})& =(\color{red}{-b}+\color{orange}{\frac{7}{5}}).(\color{green}{p}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(\frac{7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{16}b+\frac{7}{5}p-\frac{7}{5}.\frac{9}{16}& \text{Uitwerken } \\ & =-bp+\frac{9}{16}b+\frac{7}{5}p-\frac{63}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-9}{10}-q)(x+\frac{-4}{17})& =(\color{red}{-q}+\color{orange}{\frac{-9}{10}}).(\color{green}{x}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{4}{17}q-\frac{9}{10}x+\frac{9}{10}.\frac{4}{17}& \text{Uitwerken } \\ & =-qx+\frac{4}{17}q-\frac{9}{10}x+\frac{36}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{4}{17}q-\frac{9}{10}x+\frac{18}{85} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-11-20 05:03:04
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