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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-3}{9}+p)(\frac{-18}{15}-b)& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{-b}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{6}{5}p+\frac{1}{3}b+\frac{1}{3}.\frac{6}{5}& \text{Uitwerken } \\ & =-bp-\frac{6}{5}p+\frac{1}{3}b+\frac{6}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{6}{5}p+\frac{1}{3}b+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-6}{20}+x)(a+\frac{3}{7})& =(\color{red}{x}+\color{orange}{\frac{-3}{10}}).(\color{green}{a}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{7}x-\frac{3}{10}a-\frac{3}{10}.\frac{3}{7}& \text{Uitwerken } \\ & =ax+\frac{3}{7}x-\frac{3}{10}a-\frac{9}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(4-q)(\frac{-20}{17}+q)& =(\color{red}{-q}+\color{orange}{4}).(\color{green}{q}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{20}{17}q+4q-4.\frac{20}{17}& \text{Uitwerken } \\ & =-q^2+(\frac{20}{17}+4)q-\frac{80}{17} & \text{Neem samen} \\ &=-q^2+\frac{88}{17}q-\frac{80}{17} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a+\frac{2}{12})(b-\frac{13}{12})& =(\color{red}{a}+\color{orange}{\frac{1}{6}}).(\color{green}{b}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{12}a+\frac{1}{6}b-\frac{1}{6}.\frac{13}{12}& \text{Uitwerken } \\ & =ab-\frac{13}{12}a+\frac{1}{6}b-\frac{13}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{2}{3}-x)(p-\frac{6}{14})& =(\color{red}{-x}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{3}{7}x+\frac{2}{3}p-\frac{2}{3}.\frac{3}{7}& \text{Uitwerken } \\ & =-px+\frac{3}{7}x+\frac{2}{3}p-\frac{6}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{3}{7}x+\frac{2}{3}p-\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-4}{5}-x)(\frac{9}{4}-q)& =(\color{red}{-x}+\color{orange}{\frac{-4}{5}}).(\color{green}{-q}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{4}x+\frac{4}{5}q-\frac{4}{5}.\frac{9}{4}& \text{Uitwerken } \\ & =qx-\frac{9}{4}x+\frac{4}{5}q-\frac{36}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{9}{4}x+\frac{4}{5}q-\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-15}{18})(\frac{-8}{18}+x)& =(\color{red}{b}+\color{orange}{\frac{5}{6}}).(\color{green}{x}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{5}{6})} . \color{green}{(x)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{4}{9}b+\frac{5}{6}x-\frac{5}{6}.\frac{4}{9}& \text{Uitwerken } \\ & =bx-\frac{4}{9}b+\frac{5}{6}x-\frac{20}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{4}{9}b+\frac{5}{6}x-\frac{10}{27} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-11}{5}+x)(x-\frac{-13}{16})& =(\color{red}{x}+\color{orange}{\frac{-11}{5}}).(\color{green}{x}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{13}{16}x-\frac{11}{5}x-\frac{11}{5}.\frac{13}{16}& \text{Uitwerken } \\ & =x^2+(\frac{13}{16}+(\frac{-11}{5}))x-(\frac{-143}{80}) & \text{Neem samen} \\ &=x^2-\frac{111}{80}x-(\frac{-143}{80}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(1+b)(q-\frac{-7}{11})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{11}b+1q+1.\frac{7}{11}& \text{Uitwerken } \\ & =bq+\frac{7}{11}b+1q+\frac{7}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+(-1))(\frac{19}{20}+q)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{20}x-1q-1.\frac{19}{20}& \text{Uitwerken } \\ & =qx+\frac{19}{20}x-1q-\frac{19}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-6}{10}+q)(b-\frac{-5}{13})& =(\color{red}{q}+\color{orange}{\frac{-3}{5}}).(\color{green}{b}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{13}q-\frac{3}{5}b-\frac{3}{5}.\frac{5}{13}& \text{Uitwerken } \\ & =bq+\frac{5}{13}q-\frac{3}{5}b-\frac{15}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{5}{13}q-\frac{3}{5}b-\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{2}{14}-x)(b+\frac{-12}{10})& =(\color{red}{-x}+\color{orange}{\frac{1}{7}}).(\color{green}{b}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{6}{5}x+\frac{1}{7}b-\frac{1}{7}.\frac{6}{5}& \text{Uitwerken } \\ & =-bx+\frac{6}{5}x+\frac{1}{7}b-\frac{6}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-05 08:20:45
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