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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{20}+b)(\frac{-1}{14}-q)& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{-q}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{14}b-\frac{1}{5}q-\frac{1}{5}.\frac{1}{14}& \text{Uitwerken } \\ & =-bq-\frac{1}{14}b-\frac{1}{5}q-\frac{1}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-9)(\frac{2}{17}-p)& =(\color{red}{q}+\color{orange}{(-9)}).(\color{green}{-p}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(-9)} . \color{green}{(-p)} + \color{orange}{(-9)} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{2}{17}q+9p-9.\frac{2}{17}& \text{Uitwerken } \\ & =-pq+\frac{2}{17}q+9p-\frac{18}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{12}{6}+b)(q-\frac{11}{9})& =(\color{red}{b}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{9}b+2q-2.\frac{11}{9}& \text{Uitwerken } \\ & =bq-\frac{11}{9}b+2q-\frac{22}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-13}{10})(\frac{-20}{4}+q)& =(\color{red}{x}+\color{orange}{\frac{13}{10}}).(\color{green}{q}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-5)} + \color{orange}{(\frac{13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = qx-5x+\frac{13}{10}q-\frac{13}{10}.5& \text{Uitwerken } \\ & =qx-5x+\frac{13}{10}q-\frac{65}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-5x+\frac{13}{10}q-\frac{13}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x+\frac{6}{17})(b-\frac{8}{18})& =(\color{red}{x}+\color{orange}{\frac{6}{17}}).(\color{green}{b}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{6}{17})} . \color{green}{(b)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{4}{9}x+\frac{6}{17}b-\frac{6}{17}.\frac{4}{9}& \text{Uitwerken } \\ & =bx-\frac{4}{9}x+\frac{6}{17}b-\frac{24}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{4}{9}x+\frac{6}{17}b-\frac{8}{51} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}((-12)-p)(p+\frac{20}{15})& =(\color{red}{-p}+\color{orange}{(-12)}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(-12)} . \color{green}{(p)} + \color{orange}{(-12)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{4}{3}p-12p-12.\frac{4}{3}& \text{Uitwerken } \\ & =-p^2+((\frac{-4}{3})+(-12))p-\frac{48}{3} & \text{Neem samen} \\ &=-p^2-\frac{40}{3}p-\frac{48}{3} & \text{Maak de som} \\ &=-p^2-\frac{40}{3}p-16 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(b+\frac{20}{14})(\frac{10}{15}+q)& =(\color{red}{b}+\color{orange}{\frac{10}{7}}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{10}{7})} . \color{green}{(q)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{3}b+\frac{10}{7}q+\frac{10}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =bq+\frac{2}{3}b+\frac{10}{7}q+\frac{20}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-1}{4})(\frac{-5}{18}+x)& =(\color{red}{p}+\color{orange}{\frac{-1}{4}}).(\color{green}{x}+\color{blue}{\frac{-5}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{18})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-5}{18})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{18}p-\frac{1}{4}x+\frac{1}{4}.\frac{5}{18}& \text{Uitwerken } \\ & =px-\frac{5}{18}p-\frac{1}{4}x+\frac{5}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+\frac{6}{19})(\frac{-3}{20}+b)& =(\color{red}{p}+\color{orange}{\frac{6}{19}}).(\color{green}{b}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{6}{19})} . \color{green}{(b)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{20}p+\frac{6}{19}b-\frac{6}{19}.\frac{3}{20}& \text{Uitwerken } \\ & =bp-\frac{3}{20}p+\frac{6}{19}b-\frac{18}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{3}{20}p+\frac{6}{19}b-\frac{9}{190} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{3}{18})(q-\frac{4}{13})& =(\color{red}{q}+\color{orange}{\frac{-1}{6}}).(\color{green}{q}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{4}{13}q-\frac{1}{6}q+\frac{1}{6}.\frac{4}{13}& \text{Uitwerken } \\ & =q^2+((\frac{-4}{13})+(\frac{-1}{6}))q+\frac{4}{78} & \text{Neem samen} \\ &=q^2-\frac{37}{78}q+\frac{4}{78} & \text{Maak de som} \\ &=q^2-\frac{37}{78}q+\frac{2}{39} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-12}{9}-q)(x-\frac{11}{16})& =(\color{red}{-q}+\color{orange}{\frac{-4}{3}}).(\color{green}{x}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{11}{16}q-\frac{4}{3}x+\frac{4}{3}.\frac{11}{16}& \text{Uitwerken } \\ & =-qx+\frac{11}{16}q-\frac{4}{3}x+\frac{44}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{11}{16}q-\frac{4}{3}x+\frac{11}{12} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{10}{19}+q)(p-\frac{13}{14})& =(\color{red}{q}+\color{orange}{\frac{10}{19}}).(\color{green}{p}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(\frac{10}{19})} . \color{green}{(p)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{14}q+\frac{10}{19}p-\frac{10}{19}.\frac{13}{14}& \text{Uitwerken } \\ & =pq-\frac{13}{14}q+\frac{10}{19}p-\frac{130}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{13}{14}q+\frac{10}{19}p-\frac{65}{133} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-03 22:50:35
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