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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-11}{7}-p)(q-\frac{-19}{7})& =(\color{red}{-p}+\color{orange}{\frac{-11}{7}}).(\color{green}{q}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(\frac{-11}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{7}p-\frac{11}{7}q-\frac{11}{7}.\frac{19}{7}& \text{Uitwerken } \\ & =-pq-\frac{19}{7}p-\frac{11}{7}q-\frac{209}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{9}{12})(\frac{-5}{19}-b)& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{-b}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{19}x-\frac{3}{4}b-\frac{3}{4}.\frac{5}{19}& \text{Uitwerken } \\ & =-bx-\frac{5}{19}x-\frac{3}{4}b-\frac{15}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{4}{17})(x-(-15))& =(\color{red}{a}+\color{orange}{\frac{-4}{17}}).(\color{green}{x}+\color{blue}{15})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(15)} + \color{orange}{(\frac{-4}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(15)}& \text{Boogjes en uitschrijven} \\ & = ax+15a-\frac{4}{17}x-\frac{4}{17}.15& \text{Uitwerken } \\ & =ax+15a-\frac{4}{17}x-\frac{60}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{5}{11})(x-(-9))& =(\color{red}{b}+\color{orange}{\frac{5}{11}}).(\color{green}{x}+\color{blue}{9})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(9)} + \color{orange}{(\frac{5}{11})} . \color{green}{(x)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = bx+9b+\frac{5}{11}x+\frac{5}{11}.9& \text{Uitwerken } \\ & =bx+9b+\frac{5}{11}x+\frac{45}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-2}{5}-q)(b-\frac{9}{6})& =(\color{red}{-q}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{2}q-\frac{2}{5}b+\frac{2}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =-bq+\frac{3}{2}q-\frac{2}{5}b+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{3}{2}q-\frac{2}{5}b+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-7}{2})(a+\frac{20}{3})& =(\color{red}{p}+\color{orange}{\frac{-7}{2}}).(\color{green}{a}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{20}{3}p-\frac{7}{2}a-\frac{7}{2}.\frac{20}{3}& \text{Uitwerken } \\ & =ap+\frac{20}{3}p-\frac{7}{2}a-\frac{140}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{20}{3}p-\frac{7}{2}a-\frac{70}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-3}{19})(a-\frac{20}{5})& =(\color{red}{b}+\color{orange}{\frac{3}{19}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-4)} + \color{orange}{(\frac{3}{19})} . \color{green}{(a)} + \color{orange}{(\frac{3}{19})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ab-4b+\frac{3}{19}a-\frac{3}{19}.4& \text{Uitwerken } \\ & =ab-4b+\frac{3}{19}a-\frac{12}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-12}{18}+a)(a+\frac{-10}{3})& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{10}{3}a-\frac{2}{3}a+\frac{2}{3}.\frac{10}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-10}{3})+(\frac{-2}{3}))a+\frac{20}{9} & \text{Neem samen} \\ &=a^2-\frac{12}{3}a+\frac{20}{9} & \text{Maak de som} \\ &=a^2-4a+\frac{20}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(b+\frac{10}{3})(\frac{5}{20}+x)& =(\color{red}{b}+\color{orange}{\frac{10}{3}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{4}b+\frac{10}{3}x+\frac{10}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =bx+\frac{1}{4}b+\frac{10}{3}x+\frac{10}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{1}{4}b+\frac{10}{3}x+\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{8}{20})(x+\frac{-9}{20})& =(\color{red}{q}+\color{orange}{\frac{-2}{5}}).(\color{green}{x}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{20}q-\frac{2}{5}x+\frac{2}{5}.\frac{9}{20}& \text{Uitwerken } \\ & =qx-\frac{9}{20}q-\frac{2}{5}x+\frac{18}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{9}{20}q-\frac{2}{5}x+\frac{9}{50} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{12}{5})(b-\frac{-16}{15})& =(\color{red}{x}+\color{orange}{\frac{-12}{5}}).(\color{green}{b}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-12}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-12}{5})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{16}{15}x-\frac{12}{5}b-\frac{12}{5}.\frac{16}{15}& \text{Uitwerken } \\ & =bx+\frac{16}{15}x-\frac{12}{5}b-\frac{192}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{16}{15}x-\frac{12}{5}b-\frac{64}{25} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{18}{12}-a)(\frac{-7}{3}-a)& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{-a}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{3}a-\frac{3}{2}a-\frac{3}{2}.\frac{7}{3}& \text{Uitwerken } \\ & =a^2+(\frac{7}{3}+(\frac{-3}{2}))a-(\frac{-21}{6}) & \text{Neem samen} \\ &=a^2+\frac{5}{6}a-(\frac{-21}{6}) & \text{Maak de som} \\ &=a^2+\frac{5}{6}a+\frac{7}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-16 14:56:41
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