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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-16}{20}+q)(x-\frac{3}{14})& =(\color{red}{q}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{14}q-\frac{4}{5}x+\frac{4}{5}.\frac{3}{14}& \text{Uitwerken } \\ & =qx-\frac{3}{14}q-\frac{4}{5}x+\frac{12}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{3}{14}q-\frac{4}{5}x+\frac{6}{35} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{4}+p)(q+\frac{-13}{14})& =(\color{red}{p}+\color{orange}{\frac{19}{4}}).(\color{green}{q}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(\frac{19}{4})} . \color{green}{(q)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{14}p+\frac{19}{4}q-\frac{19}{4}.\frac{13}{14}& \text{Uitwerken } \\ & =pq-\frac{13}{14}p+\frac{19}{4}q-\frac{247}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{2}{17}+x)(a+\frac{-18}{7})& =(\color{red}{x}+\color{orange}{\frac{2}{17}}).(\color{green}{a}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{2}{17})} . \color{green}{(a)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{18}{7}x+\frac{2}{17}a-\frac{2}{17}.\frac{18}{7}& \text{Uitwerken } \\ & =ax-\frac{18}{7}x+\frac{2}{17}a-\frac{36}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-12}{18})(p+\frac{-8}{10})& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{4}{5}p-\frac{2}{3}p+\frac{2}{3}.\frac{4}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-4}{5})+(\frac{-2}{3}))p+\frac{8}{15} & \text{Neem samen} \\ &=p^2-\frac{22}{15}p+\frac{8}{15} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{18}-q)(\frac{13}{14}+a)& =(\color{red}{-q}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{13}{14}q+\frac{1}{2}a+\frac{1}{2}.\frac{13}{14}& \text{Uitwerken } \\ & =-aq-\frac{13}{14}q+\frac{1}{2}a+\frac{13}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{5}{18})(\frac{15}{12}-q)& =(\color{red}{q}+\color{orange}{\frac{5}{18}}).(\color{green}{-q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{5}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{5}{4}q-\frac{5}{18}q+\frac{5}{18}.\frac{5}{4}& \text{Uitwerken } \\ & =-q^2+(\frac{5}{4}+(\frac{-5}{18}))q+(\frac{-25}{72}) & \text{Neem samen} \\ &=-q^2+\frac{35}{36}q+(\frac{-25}{72}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b+2)(\frac{-16}{3}-x)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{-x}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(2)} . \color{green}{(-x)} + \color{orange}{(2)} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{16}{3}b-2x-2.\frac{16}{3}& \text{Uitwerken } \\ & =-bx-\frac{16}{3}b-2x-\frac{32}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{17}{2}+q)(a+\frac{16}{12})& =(\color{red}{q}+\color{orange}{\frac{17}{2}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{17}{2})} . \color{green}{(a)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{3}q+\frac{17}{2}a+\frac{17}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =aq+\frac{4}{3}q+\frac{17}{2}a+\frac{68}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{4}{3}q+\frac{17}{2}a+\frac{34}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{3}{16})(\frac{13}{3}-q)& =(\color{red}{x}+\color{orange}{\frac{3}{16}}).(\color{green}{-q}+\color{blue}{\frac{13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{13}{3})} + \color{orange}{(\frac{3}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{13}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{3}x-\frac{3}{16}q+\frac{3}{16}.\frac{13}{3}& \text{Uitwerken } \\ & =-qx+\frac{13}{3}x-\frac{3}{16}q+\frac{39}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{13}{3}x-\frac{3}{16}q+\frac{13}{16} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+3)(x-\frac{15}{2})& =(\color{red}{p}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{15}{2}p+3x-3.\frac{15}{2}& \text{Uitwerken } \\ & =px-\frac{15}{2}p+3x-\frac{45}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-11}{2})(p+\frac{-7}{15})& =(\color{red}{b}+\color{orange}{\frac{11}{2}}).(\color{green}{p}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{11}{2})} . \color{green}{(p)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{15}b+\frac{11}{2}p-\frac{11}{2}.\frac{7}{15}& \text{Uitwerken } \\ & =bp-\frac{7}{15}b+\frac{11}{2}p-\frac{77}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{12}-x)(p-\frac{7}{13})& =(\color{red}{-x}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{13}x+\frac{3}{4}p-\frac{3}{4}.\frac{7}{13}& \text{Uitwerken } \\ & =-px+\frac{7}{13}x+\frac{3}{4}p-\frac{21}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-10 21:56:47
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