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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-17}{20})(b+\frac{2}{18})& =(\color{red}{b}+\color{orange}{\frac{-17}{20}}).(\color{green}{b}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{9}b-\frac{17}{20}b-\frac{17}{20}.\frac{1}{9}& \text{Uitwerken } \\ & =b^2+(\frac{1}{9}+(\frac{-17}{20}))b-(\frac{-17}{180}) & \text{Neem samen} \\ &=b^2-\frac{133}{180}b-(\frac{-17}{180}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(p+\frac{20}{7})(p-\frac{19}{4})& =(\color{red}{p}+\color{orange}{\frac{20}{7}}).(\color{green}{p}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{20}{7})} . \color{green}{(p)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{19}{4}p+\frac{20}{7}p-\frac{20}{7}.\frac{19}{4}& \text{Uitwerken } \\ & =p^2+((\frac{-19}{4})+\frac{20}{7})p-(\frac{-380}{28}) & \text{Neem samen} \\ &=p^2-\frac{53}{28}p-(\frac{-380}{28}) & \text{Maak de som} \\ &=p^2-\frac{53}{28}p+\frac{95}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(a-(-2))(b+13)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{b}+\color{blue}{13})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(13)} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = ab+13a+2b+2.13& \text{Uitwerken } \\ & =ab+13a+2b+26 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{6}{14})(p+\frac{-11}{19})& =(\color{red}{b}+\color{orange}{\frac{3}{7}}).(\color{green}{p}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{19}b+\frac{3}{7}p-\frac{3}{7}.\frac{11}{19}& \text{Uitwerken } \\ & =bp-\frac{11}{19}b+\frac{3}{7}p-\frac{33}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-2}{9}+x)(\frac{6}{11}+x)& =(\color{red}{x}+\color{orange}{\frac{-2}{9}}).(\color{green}{x}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{6}{11}x-\frac{2}{9}x-\frac{2}{9}.\frac{6}{11}& \text{Uitwerken } \\ & =x^2+(\frac{6}{11}+(\frac{-2}{9}))x-(\frac{-12}{99}) & \text{Neem samen} \\ &=x^2+\frac{32}{99}x-(\frac{-12}{99}) & \text{Maak de som} \\ &=x^2+\frac{32}{99}x+\frac{4}{33} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(\frac{-6}{12}-a)(q+\frac{-6}{17})& =(\color{red}{-a}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{6}{17}a-\frac{1}{2}q+\frac{1}{2}.\frac{6}{17}& \text{Uitwerken } \\ & =-aq+\frac{6}{17}a-\frac{1}{2}q+\frac{6}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{6}{17}a-\frac{1}{2}q+\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-17}{6})(\frac{11}{20}-b)& =(\color{red}{b}+\color{orange}{\frac{17}{6}}).(\color{green}{-b}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{17}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{11}{20}b-\frac{17}{6}b+\frac{17}{6}.\frac{11}{20}& \text{Uitwerken } \\ & =-b^2+(\frac{11}{20}+(\frac{-17}{6}))b+(\frac{-187}{120}) & \text{Neem samen} \\ &=-b^2-\frac{137}{60}b+(\frac{-187}{120}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{20}{10}+b)(\frac{3}{10}-a)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{-a}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(2)} . \color{green}{(-a)} + \color{orange}{(2)} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{10}b-2a+2.\frac{3}{10}& \text{Uitwerken } \\ & =-ab+\frac{3}{10}b-2a+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{3}{10}b-2a+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-18}{5})(\frac{14}{12}+a)& =(\color{red}{x}+\color{orange}{\frac{18}{5}}).(\color{green}{a}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{18}{5})} . \color{green}{(a)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{6}x+\frac{18}{5}a+\frac{18}{5}.\frac{7}{6}& \text{Uitwerken } \\ & =ax+\frac{7}{6}x+\frac{18}{5}a+\frac{126}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{7}{6}x+\frac{18}{5}a+\frac{21}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{1}{20})(q-\frac{-11}{13})& =(\color{red}{p}+\color{orange}{\frac{-1}{20}}).(\color{green}{q}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{-1}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{13}p-\frac{1}{20}q-\frac{1}{20}.\frac{11}{13}& \text{Uitwerken } \\ & =pq+\frac{11}{13}p-\frac{1}{20}q-\frac{11}{260} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-5}{14}-x)(\frac{-7}{14}+p)& =(\color{red}{-x}+\color{orange}{\frac{-5}{14}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{2}x-\frac{5}{14}p+\frac{5}{14}.\frac{1}{2}& \text{Uitwerken } \\ & =-px+\frac{1}{2}x-\frac{5}{14}p+\frac{5}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-17}{16}+q)(\frac{9}{16}+p)& =(\color{red}{q}+\color{orange}{\frac{-17}{16}}).(\color{green}{p}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{16}q-\frac{17}{16}p-\frac{17}{16}.\frac{9}{16}& \text{Uitwerken } \\ & =pq+\frac{9}{16}q-\frac{17}{16}p-\frac{153}{256} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-22 05:44:44
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