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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{7}{9})(q-\frac{17}{17})& =(\color{red}{x}+\color{orange}{\frac{7}{9}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1x+\frac{7}{9}q-\frac{7}{9}.1& \text{Uitwerken } \\ & =qx-1x+\frac{7}{9}q-\frac{7}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(14-q)(b-\frac{8}{15})& =(\color{red}{-q}+\color{orange}{14}).(\color{green}{b}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(14)} . \color{green}{(b)} + \color{orange}{(14)} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{8}{15}q+14b-14.\frac{8}{15}& \text{Uitwerken } \\ & =-bq+\frac{8}{15}q+14b-\frac{112}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-20}{19}+p)(p-\frac{-2}{3})& =(\color{red}{p}+\color{orange}{\frac{-20}{19}}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-20}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{2}{3}p-\frac{20}{19}p-\frac{20}{19}.\frac{2}{3}& \text{Uitwerken } \\ & =p^2+(\frac{2}{3}+(\frac{-20}{19}))p-(\frac{-40}{57}) & \text{Neem samen} \\ &=p^2-\frac{22}{57}p-(\frac{-40}{57}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-8}{19})(\frac{-2}{12}-b)& =(\color{red}{p}+\color{orange}{\frac{-8}{19}}).(\color{green}{-b}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-8}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{6}p+\frac{8}{19}b+\frac{8}{19}.\frac{1}{6}& \text{Uitwerken } \\ & =-bp-\frac{1}{6}p+\frac{8}{19}b+\frac{8}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{1}{6}p+\frac{8}{19}b+\frac{4}{57} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{20}{12}-q)(\frac{3}{13}-x)& =(\color{red}{-q}+\color{orange}{\frac{5}{3}}).(\color{green}{-x}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{13}q-\frac{5}{3}x+\frac{5}{3}.\frac{3}{13}& \text{Uitwerken } \\ & =qx-\frac{3}{13}q-\frac{5}{3}x+\frac{15}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{3}{13}q-\frac{5}{3}x+\frac{5}{13} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{20}{17})(\frac{10}{20}-b)& =(\color{red}{b}+\color{orange}{\frac{-20}{17}}).(\color{green}{-b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{2}b+\frac{20}{17}b-\frac{20}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{2}+\frac{20}{17})b-\frac{20}{34} & \text{Neem samen} \\ &=-b^2+\frac{57}{34}b-\frac{20}{34} & \text{Maak de som} \\ &=-b^2+\frac{57}{34}b-\frac{10}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-1}{16})(a+\frac{-4}{12})& =(\color{red}{p}+\color{orange}{\frac{1}{16}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{1}{16})} . \color{green}{(a)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{3}p+\frac{1}{16}a-\frac{1}{16}.\frac{1}{3}& \text{Uitwerken } \\ & =ap-\frac{1}{3}p+\frac{1}{16}a-\frac{1}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-8}{7})(x-\frac{-15}{6})& =(\color{red}{p}+\color{orange}{\frac{-8}{7}}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{2}p-\frac{8}{7}x-\frac{8}{7}.\frac{5}{2}& \text{Uitwerken } \\ & =px+\frac{5}{2}p-\frac{8}{7}x-\frac{40}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{5}{2}p-\frac{8}{7}x-\frac{20}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{16}{15}+b)(\frac{19}{19}+x)& =(\color{red}{b}+\color{orange}{\frac{16}{15}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{16}{15})} . \color{green}{(x)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1b+\frac{16}{15}x+\frac{16}{15}.1& \text{Uitwerken } \\ & =bx+1b+\frac{16}{15}x+\frac{16}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{11}{2}-b)(\frac{-3}{15}+b)& =(\color{red}{-b}+\color{orange}{\frac{11}{2}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{11}{2})} . \color{green}{(b)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{5}b+\frac{11}{2}b-\frac{11}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{5}+\frac{11}{2})b-\frac{11}{10} & \text{Neem samen} \\ &=-b^2+\frac{57}{10}b-\frac{11}{10} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{15}+b)(\frac{-19}{14}+x)& =(\color{red}{b}+\color{orange}{\frac{-13}{15}}).(\color{green}{x}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{14}b-\frac{13}{15}x+\frac{13}{15}.\frac{19}{14}& \text{Uitwerken } \\ & =bx-\frac{19}{14}b-\frac{13}{15}x+\frac{247}{210} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{9}+b)(q+\frac{8}{17})& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{q}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{8}{17}b-\frac{5}{3}q-\frac{5}{3}.\frac{8}{17}& \text{Uitwerken } \\ & =bq+\frac{8}{17}b-\frac{5}{3}q-\frac{40}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-11-09 01:14:49
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