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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-20}{4}-b)(\frac{16}{19}+x)& =(\color{red}{-b}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{16}{19}b-5x-5.\frac{16}{19}& \text{Uitwerken } \\ & =-bx-\frac{16}{19}b-5x-\frac{80}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{6}{15}-q)(\frac{15}{4}-b)& =(\color{red}{-q}+\color{orange}{\frac{2}{5}}).(\color{green}{-b}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{15}{4}q-\frac{2}{5}b+\frac{2}{5}.\frac{15}{4}& \text{Uitwerken } \\ & =bq-\frac{15}{4}q-\frac{2}{5}b+\frac{30}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{15}{4}q-\frac{2}{5}b+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-8}{15})(x+\frac{1}{6})& =(\color{red}{q}+\color{orange}{\frac{8}{15}}).(\color{green}{x}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{8}{15})} . \color{green}{(x)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{6}q+\frac{8}{15}x+\frac{8}{15}.\frac{1}{6}& \text{Uitwerken } \\ & =qx+\frac{1}{6}q+\frac{8}{15}x+\frac{8}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{6}q+\frac{8}{15}x+\frac{4}{45} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-18}{14})(\frac{-16}{9}-a)& =(\color{red}{q}+\color{orange}{\frac{-9}{7}}).(\color{green}{-a}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{16}{9}q+\frac{9}{7}a+\frac{9}{7}.\frac{16}{9}& \text{Uitwerken } \\ & =-aq-\frac{16}{9}q+\frac{9}{7}a+\frac{144}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{16}{9}q+\frac{9}{7}a+\frac{16}{7} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-3}{14})(x-\frac{3}{8})& =(\color{red}{b}+\color{orange}{\frac{3}{14}}).(\color{green}{x}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{3}{14})} . \color{green}{(x)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{8}b+\frac{3}{14}x-\frac{3}{14}.\frac{3}{8}& \text{Uitwerken } \\ & =bx-\frac{3}{8}b+\frac{3}{14}x-\frac{9}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{9}{8})(q-\frac{-9}{5})& =(\color{red}{a}+\color{orange}{\frac{9}{8}}).(\color{green}{q}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{5}a+\frac{9}{8}q+\frac{9}{8}.\frac{9}{5}& \text{Uitwerken } \\ & =aq+\frac{9}{5}a+\frac{9}{8}q+\frac{81}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-13}{17}-a)(q-\frac{11}{20})& =(\color{red}{-a}+\color{orange}{\frac{-13}{17}}).(\color{green}{q}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{11}{20}a-\frac{13}{17}q+\frac{13}{17}.\frac{11}{20}& \text{Uitwerken } \\ & =-aq+\frac{11}{20}a-\frac{13}{17}q+\frac{143}{340} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{17}{10})(p+\frac{7}{15})& =(\color{red}{x}+\color{orange}{\frac{-17}{10}}).(\color{green}{p}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{15}x-\frac{17}{10}p-\frac{17}{10}.\frac{7}{15}& \text{Uitwerken } \\ & =px+\frac{7}{15}x-\frac{17}{10}p-\frac{119}{150} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{15}{9})(\frac{-2}{12}+a)& =(\color{red}{b}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{6}b+\frac{5}{3}a-\frac{5}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =ab-\frac{1}{6}b+\frac{5}{3}a-\frac{5}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-13}{6}-a)(\frac{-8}{13}-q)& =(\color{red}{-a}+\color{orange}{\frac{-13}{6}}).(\color{green}{-q}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{13}a+\frac{13}{6}q+\frac{13}{6}.\frac{8}{13}& \text{Uitwerken } \\ & =aq+\frac{8}{13}a+\frac{13}{6}q+\frac{104}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{8}{13}a+\frac{13}{6}q+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-17}{4}-x)(b+\frac{16}{6})& =(\color{red}{-x}+\color{orange}{\frac{-17}{4}}).(\color{green}{b}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{8}{3}x-\frac{17}{4}b-\frac{17}{4}.\frac{8}{3}& \text{Uitwerken } \\ & =-bx-\frac{8}{3}x-\frac{17}{4}b-\frac{136}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{8}{3}x-\frac{17}{4}b-\frac{34}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-12}{18})(\frac{-18}{6}-a)& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{-a}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -aa-3a+\frac{2}{3}a+\frac{2}{3}.3& \text{Uitwerken } \\ & =-a^2+((-3)+\frac{2}{3})a+(\frac{-6}{3}) & \text{Neem samen} \\ &=-a^2-\frac{7}{3}a+(\frac{-6}{3}) & \text{Maak de som} \\ &=-a^2-\frac{7}{3}a+(-2) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-07 23:03:12
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