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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-2}{19}-a)(b+\frac{15}{20})& =(\color{red}{-a}+\color{orange}{\frac{-2}{19}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-2}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{4}a-\frac{2}{19}b-\frac{2}{19}.\frac{3}{4}& \text{Uitwerken } \\ & =-ab-\frac{3}{4}a-\frac{2}{19}b-\frac{6}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{3}{4}a-\frac{2}{19}b-\frac{3}{38} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x-\frac{18}{3})(p+\frac{13}{13})& =(\color{red}{x}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1x-6p-6.1& \text{Uitwerken } \\ & =px+1x-6p-6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{7}-x)(\frac{-8}{17}-b)& =(\color{red}{-x}+\color{orange}{(-2)}).(\color{green}{-b}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(-2)} . \color{green}{(-b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{8}{17}x+2b+2.\frac{8}{17}& \text{Uitwerken } \\ & =bx+\frac{8}{17}x+2b+\frac{16}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{11}-b)(x-\frac{1}{3})& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{3}b+1x-1.\frac{1}{3}& \text{Uitwerken } \\ & =-bx+\frac{1}{3}b+1x-\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{19}{12})(\frac{-8}{18}+p)& =(\color{red}{x}+\color{orange}{\frac{-19}{12}}).(\color{green}{p}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{9}x-\frac{19}{12}p+\frac{19}{12}.\frac{4}{9}& \text{Uitwerken } \\ & =px-\frac{4}{9}x-\frac{19}{12}p+\frac{76}{108} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{4}{9}x-\frac{19}{12}p+\frac{19}{27} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-12}{6}-a)(\frac{-19}{15}-p)& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{15}a+2p+2.\frac{19}{15}& \text{Uitwerken } \\ & =ap+\frac{19}{15}a+2p+\frac{38}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{2}{11})(x-\frac{-15}{8})& =(\color{red}{p}+\color{orange}{\frac{-2}{11}}).(\color{green}{x}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{15}{8}p-\frac{2}{11}x-\frac{2}{11}.\frac{15}{8}& \text{Uitwerken } \\ & =px+\frac{15}{8}p-\frac{2}{11}x-\frac{30}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{15}{8}p-\frac{2}{11}x-\frac{15}{44} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{20}+q)(b-\frac{7}{17})& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{b}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(\frac{3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{17}q+\frac{3}{5}b-\frac{3}{5}.\frac{7}{17}& \text{Uitwerken } \\ & =bq-\frac{7}{17}q+\frac{3}{5}b-\frac{21}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{18}{17}-q)(a-\frac{-6}{5})& =(\color{red}{-q}+\color{orange}{\frac{18}{17}}).(\color{green}{a}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{18}{17})} . \color{green}{(a)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{6}{5}q+\frac{18}{17}a+\frac{18}{17}.\frac{6}{5}& \text{Uitwerken } \\ & =-aq-\frac{6}{5}q+\frac{18}{17}a+\frac{108}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{5}{3}-q)(a+\frac{4}{5})& =(\color{red}{-q}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{4}{5}q+\frac{5}{3}a+\frac{5}{3}.\frac{4}{5}& \text{Uitwerken } \\ & =-aq-\frac{4}{5}q+\frac{5}{3}a+\frac{20}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{4}{5}q+\frac{5}{3}a+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-15}{13}+x)(\frac{2}{15}-p)& =(\color{red}{x}+\color{orange}{\frac{-15}{13}}).(\color{green}{-p}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{15}x+\frac{15}{13}p-\frac{15}{13}.\frac{2}{15}& \text{Uitwerken } \\ & =-px+\frac{2}{15}x+\frac{15}{13}p-\frac{30}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{2}{15}x+\frac{15}{13}p-\frac{2}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x+\frac{16}{7})(\frac{4}{18}+p)& =(\color{red}{x}+\color{orange}{\frac{16}{7}}).(\color{green}{p}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{16}{7})} . \color{green}{(p)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{2}{9}x+\frac{16}{7}p+\frac{16}{7}.\frac{2}{9}& \text{Uitwerken } \\ & =px+\frac{2}{9}x+\frac{16}{7}p+\frac{32}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-26 05:53:29
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