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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{14}{13})(\frac{16}{19}+b)& =(\color{red}{b}+\color{orange}{\frac{14}{13}}).(\color{green}{b}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{14}{13})} . \color{green}{(b)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{16}{19}b+\frac{14}{13}b+\frac{14}{13}.\frac{16}{19}& \text{Uitwerken } \\ & =b^2+(\frac{16}{19}+\frac{14}{13})b+\frac{224}{247} & \text{Neem samen} \\ &=b^2+\frac{474}{247}b+\frac{224}{247} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{3}-b)(\frac{-6}{10}-p)& =(\color{red}{-b}+\color{orange}{\frac{8}{3}}).(\color{green}{-p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{8}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{5}b-\frac{8}{3}p-\frac{8}{3}.\frac{3}{5}& \text{Uitwerken } \\ & =bp+\frac{3}{5}b-\frac{8}{3}p-\frac{24}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{3}{5}b-\frac{8}{3}p-\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{16}{13})(q-\frac{-15}{17})& =(\color{red}{b}+\color{orange}{\frac{-16}{13}}).(\color{green}{q}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{17}b-\frac{16}{13}q-\frac{16}{13}.\frac{15}{17}& \text{Uitwerken } \\ & =bq+\frac{15}{17}b-\frac{16}{13}q-\frac{240}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-18}{18}-p)(x+\frac{-1}{15})& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{15}p-1x+1.\frac{1}{15}& \text{Uitwerken } \\ & =-px+\frac{1}{15}p-1x+\frac{1}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{3}-a)(\frac{20}{10}+a)& =(\color{red}{-a}+\color{orange}{(-5)}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(2)} + \color{orange}{(-5)} . \color{green}{(a)} + \color{orange}{(-5)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -aa-2a-5a-5.2& \text{Uitwerken } \\ & =-a^2+((-2)+(-5))a-10 & \text{Neem samen} \\ &=-a^2-7a-10 & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-20}{13}+p)(\frac{-11}{16}+a)& =(\color{red}{p}+\color{orange}{\frac{-20}{13}}).(\color{green}{a}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{16}p-\frac{20}{13}a+\frac{20}{13}.\frac{11}{16}& \text{Uitwerken } \\ & =ap-\frac{11}{16}p-\frac{20}{13}a+\frac{220}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{11}{16}p-\frac{20}{13}a+\frac{55}{52} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+\frac{19}{17})(\frac{6}{5}+p)& =(\color{red}{p}+\color{orange}{\frac{19}{17}}).(\color{green}{p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{19}{17})} . \color{green}{(p)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{6}{5}p+\frac{19}{17}p+\frac{19}{17}.\frac{6}{5}& \text{Uitwerken } \\ & =p^2+(\frac{6}{5}+\frac{19}{17})p+\frac{114}{85} & \text{Neem samen} \\ &=p^2+\frac{197}{85}p+\frac{114}{85} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-19}{6}+q)(p-\frac{1}{11})& =(\color{red}{q}+\color{orange}{\frac{-19}{6}}).(\color{green}{p}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{11}q-\frac{19}{6}p+\frac{19}{6}.\frac{1}{11}& \text{Uitwerken } \\ & =pq-\frac{1}{11}q-\frac{19}{6}p+\frac{19}{66} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{19}{2})(q-\frac{-17}{19})& =(\color{red}{b}+\color{orange}{\frac{-19}{2}}).(\color{green}{q}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{19}b-\frac{19}{2}q-\frac{19}{2}.\frac{17}{19}& \text{Uitwerken } \\ & =bq+\frac{17}{19}b-\frac{19}{2}q-\frac{323}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{17}{19}b-\frac{19}{2}q-\frac{17}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-11}{13})(b-\frac{6}{20})& =(\color{red}{q}+\color{orange}{\frac{-11}{13}}).(\color{green}{b}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{10}q-\frac{11}{13}b+\frac{11}{13}.\frac{3}{10}& \text{Uitwerken } \\ & =bq-\frac{3}{10}q-\frac{11}{13}b+\frac{33}{130} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{4}-p)(\frac{-4}{18}+a)& =(\color{red}{-p}+\color{orange}{\frac{-13}{4}}).(\color{green}{a}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{9}p-\frac{13}{4}a+\frac{13}{4}.\frac{2}{9}& \text{Uitwerken } \\ & =-ap+\frac{2}{9}p-\frac{13}{4}a+\frac{26}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{2}{9}p-\frac{13}{4}a+\frac{13}{18} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-4}{6})(x+\frac{14}{8})& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{4}q-\frac{2}{3}x-\frac{2}{3}.\frac{7}{4}& \text{Uitwerken } \\ & =qx+\frac{7}{4}q-\frac{2}{3}x-\frac{14}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{7}{4}q-\frac{2}{3}x-\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-30 01:12:15
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