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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+(-13))(b-\frac{-9}{2})& =(\color{red}{b}+\color{orange}{(-13)}).(\color{green}{b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(-13)} . \color{green}{(b)} + \color{orange}{(-13)} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{9}{2}b-13b-13.\frac{9}{2}& \text{Uitwerken } \\ & =b^2+(\frac{9}{2}+(-13))b-(\frac{-117}{2}) & \text{Neem samen} \\ &=b^2-\frac{17}{2}b-(\frac{-117}{2}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-5}{4})(x-\frac{-13}{11})& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{x}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{11}p-\frac{5}{4}x-\frac{5}{4}.\frac{13}{11}& \text{Uitwerken } \\ & =px+\frac{13}{11}p-\frac{5}{4}x-\frac{65}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{10}{2})(q+\frac{-10}{11})& =(\color{red}{x}+\color{orange}{(-5)}).(\color{green}{q}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(-5)} . \color{green}{(q)} + \color{orange}{(-5)} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{10}{11}x-5q+5.\frac{10}{11}& \text{Uitwerken } \\ & =qx-\frac{10}{11}x-5q+\frac{50}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{18}{15})((-7)+b)& =(\color{red}{q}+\color{orange}{\frac{6}{5}}).(\color{green}{b}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-7)} + \color{orange}{(\frac{6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = bq-7q+\frac{6}{5}b-\frac{6}{5}.7& \text{Uitwerken } \\ & =bq-7q+\frac{6}{5}b-\frac{42}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{6}{15}+x)(\frac{-3}{9}+a)& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{3}x+\frac{2}{5}a-\frac{2}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =ax-\frac{1}{3}x+\frac{2}{5}a-\frac{2}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-5}{10}-x)(x+\frac{3}{10})& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{3}{10}x-\frac{1}{2}x-\frac{1}{2}.\frac{3}{10}& \text{Uitwerken } \\ & =-x^2+((\frac{-3}{10})+(\frac{-1}{2}))x-\frac{3}{20} & \text{Neem samen} \\ &=-x^2-\frac{8}{10}x-\frac{3}{20} & \text{Maak de som} \\ &=-x^2-\frac{4}{5}x-\frac{3}{20} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-11}{19})(\frac{1}{19}+a)& =(\color{red}{b}+\color{orange}{\frac{-11}{19}}).(\color{green}{a}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{19}b-\frac{11}{19}a-\frac{11}{19}.\frac{1}{19}& \text{Uitwerken } \\ & =ab+\frac{1}{19}b-\frac{11}{19}a-\frac{11}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-8}{8}-x)(q-\frac{11}{13})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{11}{13}x-1q+1.\frac{11}{13}& \text{Uitwerken } \\ & =-qx+\frac{11}{13}x-1q+\frac{11}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{-9}{5})(\frac{-17}{18}+x)& =(\color{red}{q}+\color{orange}{\frac{-9}{5}}).(\color{green}{x}+\color{blue}{\frac{-17}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{18})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{-17}{18})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{18}q-\frac{9}{5}x+\frac{9}{5}.\frac{17}{18}& \text{Uitwerken } \\ & =qx-\frac{17}{18}q-\frac{9}{5}x+\frac{153}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{17}{18}q-\frac{9}{5}x+\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{4}+p)(x+\frac{12}{14})& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{6}{7}p+\frac{3}{4}x+\frac{3}{4}.\frac{6}{7}& \text{Uitwerken } \\ & =px+\frac{6}{7}p+\frac{3}{4}x+\frac{18}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{6}{7}p+\frac{3}{4}x+\frac{9}{14} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-6}{2})(p+\frac{13}{3})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{13}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{3})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{13}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{3}b-3p-3.\frac{13}{3}& \text{Uitwerken } \\ & =bp+\frac{13}{3}b-3p-\frac{39}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{13}{3}b-3p-13 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{11}{3}-q)(b-\frac{-19}{10})& =(\color{red}{-q}+\color{orange}{\frac{11}{3}}).(\color{green}{b}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{11}{3})} . \color{green}{(b)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{19}{10}q+\frac{11}{3}b+\frac{11}{3}.\frac{19}{10}& \text{Uitwerken } \\ & =-bq-\frac{19}{10}q+\frac{11}{3}b+\frac{209}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-10 12:22:18
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