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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(3-q)(\frac{-15}{18}-b)& =(\color{red}{-q}+\color{orange}{3}).(\color{green}{-b}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(3)} . \color{green}{(-b)} + \color{orange}{(3)} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{6}q-3b-3.\frac{5}{6}& \text{Uitwerken } \\ & =bq+\frac{5}{6}q-3b-\frac{15}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{5}{6}q-3b-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{15}{14})(\frac{-13}{5}-a)& =(\color{red}{a}+\color{orange}{\frac{-15}{14}}).(\color{green}{-a}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{13}{5}a+\frac{15}{14}a+\frac{15}{14}.\frac{13}{5}& \text{Uitwerken } \\ & =-a^2+((\frac{-13}{5})+\frac{15}{14})a+(\frac{-195}{70}) & \text{Neem samen} \\ &=-a^2-\frac{107}{70}a+(\frac{-195}{70}) & \text{Maak de som} \\ &=-a^2-\frac{107}{70}a+(\frac{-39}{14}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-13}{9}+b)(b-\frac{-9}{12})& =(\color{red}{b}+\color{orange}{\frac{-13}{9}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{4}b-\frac{13}{9}b-\frac{13}{9}.\frac{3}{4}& \text{Uitwerken } \\ & =b^2+(\frac{3}{4}+(\frac{-13}{9}))b-(\frac{-39}{36}) & \text{Neem samen} \\ &=b^2-\frac{25}{36}b-(\frac{-39}{36}) & \text{Maak de som} \\ &=b^2-\frac{25}{36}b+\frac{13}{12} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(x+12)(b-\frac{-17}{15})& =(\color{red}{x}+\color{orange}{12}).(\color{green}{b}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(12)} . \color{green}{(b)} + \color{orange}{(12)} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{15}x+12b+12.\frac{17}{15}& \text{Uitwerken } \\ & =bx+\frac{17}{15}x+12b+\frac{204}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{17}{15}x+12b+\frac{68}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{20}{9})(\frac{-13}{4}-p)& =(\color{red}{a}+\color{orange}{\frac{20}{9}}).(\color{green}{-p}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{20}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{4}a-\frac{20}{9}p-\frac{20}{9}.\frac{13}{4}& \text{Uitwerken } \\ & =-ap-\frac{13}{4}a-\frac{20}{9}p-\frac{260}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{13}{4}a-\frac{20}{9}p-\frac{65}{9} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{16}{13}+p)(x-\frac{-7}{4})& =(\color{red}{p}+\color{orange}{\frac{16}{13}}).(\color{green}{x}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{16}{13})} . \color{green}{(x)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{4}p+\frac{16}{13}x+\frac{16}{13}.\frac{7}{4}& \text{Uitwerken } \\ & =px+\frac{7}{4}p+\frac{16}{13}x+\frac{112}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{7}{4}p+\frac{16}{13}x+\frac{28}{13} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q-\frac{16}{20})(a+\frac{-11}{13})& =(\color{red}{q}+\color{orange}{\frac{-4}{5}}).(\color{green}{a}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{13}q-\frac{4}{5}a+\frac{4}{5}.\frac{11}{13}& \text{Uitwerken } \\ & =aq-\frac{11}{13}q-\frac{4}{5}a+\frac{44}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-19}{11})(\frac{9}{7}+x)& =(\color{red}{b}+\color{orange}{\frac{-19}{11}}).(\color{green}{x}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{7}b-\frac{19}{11}x-\frac{19}{11}.\frac{9}{7}& \text{Uitwerken } \\ & =bx+\frac{9}{7}b-\frac{19}{11}x-\frac{171}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-(-4))(x+\frac{9}{9})& =(\color{red}{x}+\color{orange}{4}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = xx+1x+4x+4.1& \text{Uitwerken } \\ & =x^2+(1+4)x+4 & \text{Neem samen} \\ &=x^2+5x+4 & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-5}{9}+q)(\frac{-9}{5}+a)& =(\color{red}{q}+\color{orange}{\frac{-5}{9}}).(\color{green}{a}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{9}{5}q-\frac{5}{9}a+\frac{5}{9}.\frac{9}{5}& \text{Uitwerken } \\ & =aq-\frac{9}{5}q-\frac{5}{9}a+\frac{45}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{9}{5}q-\frac{5}{9}a+1 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{13}-x)(\frac{6}{17}+p)& =(\color{red}{-x}+\color{orange}{\frac{-14}{13}}).(\color{green}{p}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{6}{17}x-\frac{14}{13}p-\frac{14}{13}.\frac{6}{17}& \text{Uitwerken } \\ & =-px-\frac{6}{17}x-\frac{14}{13}p-\frac{84}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{19}{2}+a)(x+\frac{-3}{2})& =(\color{red}{a}+\color{orange}{\frac{19}{2}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{19}{2})} . \color{green}{(x)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{2}a+\frac{19}{2}x-\frac{19}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =ax-\frac{3}{2}a+\frac{19}{2}x-\frac{57}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-01 03:31:34
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