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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{1}{9}+x)(\frac{19}{19}-p)& =(\color{red}{x}+\color{orange}{\frac{1}{9}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -px+1x-\frac{1}{9}p+\frac{1}{9}.1& \text{Uitwerken } \\ & =-px+1x-\frac{1}{9}p+\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-(-7))(\frac{19}{13}-p)& =(\color{red}{b}+\color{orange}{7}).(\color{green}{-p}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(7)} . \color{green}{(-p)} + \color{orange}{(7)} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{19}{13}b-7p+7.\frac{19}{13}& \text{Uitwerken } \\ & =-bp+\frac{19}{13}b-7p+\frac{133}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-6}{3}+p)(b+\frac{-2}{14})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{7}p-2b+2.\frac{1}{7}& \text{Uitwerken } \\ & =bp-\frac{1}{7}p-2b+\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{12}{10})(\frac{-2}{16}-q)& =(\color{red}{p}+\color{orange}{\frac{-6}{5}}).(\color{green}{-q}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{8}p+\frac{6}{5}q+\frac{6}{5}.\frac{1}{8}& \text{Uitwerken } \\ & =-pq-\frac{1}{8}p+\frac{6}{5}q+\frac{6}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{1}{8}p+\frac{6}{5}q+\frac{3}{20} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p+\frac{15}{14})(b-\frac{9}{9})& =(\color{red}{p}+\color{orange}{\frac{15}{14}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{15}{14})} . \color{green}{(b)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bp-1p+\frac{15}{14}b-\frac{15}{14}.1& \text{Uitwerken } \\ & =bp-1p+\frac{15}{14}b-\frac{15}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-2}{18})(\frac{-9}{7}+p)& =(\color{red}{p}+\color{orange}{\frac{1}{9}}).(\color{green}{p}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{9}{7}p+\frac{1}{9}p-\frac{1}{9}.\frac{9}{7}& \text{Uitwerken } \\ & =p^2+((\frac{-9}{7})+\frac{1}{9})p-(\frac{-9}{63}) & \text{Neem samen} \\ &=p^2-\frac{74}{63}p-(\frac{-9}{63}) & \text{Maak de som} \\ &=p^2-\frac{74}{63}p+\frac{1}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{-15}{14}-b)(\frac{20}{18}+a)& =(\color{red}{-b}+\color{orange}{\frac{-15}{14}}).(\color{green}{a}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{10}{9}b-\frac{15}{14}a-\frac{15}{14}.\frac{10}{9}& \text{Uitwerken } \\ & =-ab-\frac{10}{9}b-\frac{15}{14}a-\frac{150}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{10}{9}b-\frac{15}{14}a-\frac{25}{21} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{15}+q)(a+\frac{12}{19})& =(\color{red}{q}+\color{orange}{\frac{-1}{5}}).(\color{green}{a}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{12}{19}q-\frac{1}{5}a-\frac{1}{5}.\frac{12}{19}& \text{Uitwerken } \\ & =aq+\frac{12}{19}q-\frac{1}{5}a-\frac{12}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{4}{4})(\frac{3}{16}-b)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{3}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{16})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{16}q-1b+1.\frac{3}{16}& \text{Uitwerken } \\ & =-bq+\frac{3}{16}q-1b+\frac{3}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{11}-b)(b-\frac{11}{14})& =(\color{red}{-b}+\color{orange}{\frac{3}{11}}).(\color{green}{b}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{3}{11})} . \color{green}{(b)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{11}{14}b+\frac{3}{11}b-\frac{3}{11}.\frac{11}{14}& \text{Uitwerken } \\ & =-b^2+(\frac{11}{14}+\frac{3}{11})b-\frac{33}{154} & \text{Neem samen} \\ &=-b^2+\frac{163}{154}b-\frac{33}{154} & \text{Maak de som} \\ &=-b^2+\frac{163}{154}b-\frac{3}{14} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-3}{9}-p)(\frac{1}{15}-p)& =(\color{red}{-p}+\color{orange}{\frac{-1}{3}}).(\color{green}{-p}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{15}p+\frac{1}{3}p-\frac{1}{3}.\frac{1}{15}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{15})+\frac{1}{3})p-(\frac{-1}{45}) & \text{Neem samen} \\ &=p^2+\frac{4}{15}p-(\frac{-1}{45}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(p-\frac{12}{8})(\frac{-1}{20}-q)& =(\color{red}{p}+\color{orange}{\frac{-3}{2}}).(\color{green}{-q}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{20}p+\frac{3}{2}q+\frac{3}{2}.\frac{1}{20}& \text{Uitwerken } \\ & =-pq-\frac{1}{20}p+\frac{3}{2}q+\frac{3}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-10 07:19:07
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