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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-15}{12})(\frac{-4}{15}-p)& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{-p}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{4}{15}a+\frac{5}{4}p+\frac{5}{4}.\frac{4}{15}& \text{Uitwerken } \\ & =-ap-\frac{4}{15}a+\frac{5}{4}p+\frac{20}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{4}{15}a+\frac{5}{4}p+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{4}{7}-b)(q+\frac{2}{8})& =(\color{red}{-b}+\color{orange}{\frac{4}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{4}b+\frac{4}{7}q+\frac{4}{7}.\frac{1}{4}& \text{Uitwerken } \\ & =-bq-\frac{1}{4}b+\frac{4}{7}q+\frac{4}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{4}b+\frac{4}{7}q+\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}((-1)-x)(a+\frac{-2}{7})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{2}{7}x-1a+1.\frac{2}{7}& \text{Uitwerken } \\ & =-ax+\frac{2}{7}x-1a+\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{14}{11})(b-(-5))& =(\color{red}{b}+\color{orange}{\frac{14}{11}}).(\color{green}{b}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(5)} + \color{orange}{(\frac{14}{11})} . \color{green}{(b)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bb+5b+\frac{14}{11}b+\frac{14}{11}.5& \text{Uitwerken } \\ & =b^2+(5+\frac{14}{11})b+\frac{70}{11} & \text{Neem samen} \\ &=b^2+\frac{69}{11}b+\frac{70}{11} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(x-\frac{16}{8})(\frac{-7}{10}+a)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{10}x-2a+2.\frac{7}{10}& \text{Uitwerken } \\ & =ax-\frac{7}{10}x-2a+\frac{14}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{7}{10}x-2a+\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{13}+q)(a-\frac{1}{4})& =(\color{red}{q}+\color{orange}{\frac{-9}{13}}).(\color{green}{a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{4}q-\frac{9}{13}a+\frac{9}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =aq-\frac{1}{4}q-\frac{9}{13}a+\frac{9}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{3}{6})(\frac{-18}{14}+p)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{7}b-\frac{1}{2}p+\frac{1}{2}.\frac{9}{7}& \text{Uitwerken } \\ & =bp-\frac{9}{7}b-\frac{1}{2}p+\frac{9}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-16}{3}-p)(\frac{17}{4}+a)& =(\color{red}{-p}+\color{orange}{\frac{-16}{3}}).(\color{green}{a}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{-16}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{4}p-\frac{16}{3}a-\frac{16}{3}.\frac{17}{4}& \text{Uitwerken } \\ & =-ap-\frac{17}{4}p-\frac{16}{3}a-\frac{272}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{17}{4}p-\frac{16}{3}a-\frac{68}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-12}{15})(\frac{-9}{6}-p)& =(\color{red}{x}+\color{orange}{\frac{-4}{5}}).(\color{green}{-p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{2}x+\frac{4}{5}p+\frac{4}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =-px-\frac{3}{2}x+\frac{4}{5}p+\frac{12}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{3}{2}x+\frac{4}{5}p+\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x+\frac{18}{10})(b-\frac{-1}{8})& =(\color{red}{x}+\color{orange}{\frac{9}{5}}).(\color{green}{b}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{9}{5})} . \color{green}{(b)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{8}x+\frac{9}{5}b+\frac{9}{5}.\frac{1}{8}& \text{Uitwerken } \\ & =bx+\frac{1}{8}x+\frac{9}{5}b+\frac{9}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(3+b)(\frac{9}{10}-b)& =(\color{red}{b}+\color{orange}{3}).(\color{green}{-b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(3)} . \color{green}{(-b)} + \color{orange}{(3)} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{9}{10}b-3b+3.\frac{9}{10}& \text{Uitwerken } \\ & =-b^2+(\frac{9}{10}+(-3))b+(\frac{-27}{10}) & \text{Neem samen} \\ &=-b^2-\frac{21}{10}b+(\frac{-27}{10}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-16}{10})(a-\frac{-20}{15})& =(\color{red}{q}+\color{orange}{\frac{-8}{5}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{3}q-\frac{8}{5}a-\frac{8}{5}.\frac{4}{3}& \text{Uitwerken } \\ & =aq+\frac{4}{3}q-\frac{8}{5}a-\frac{32}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-05 01:18:34
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