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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-6}{12}+p)(q-\frac{-3}{20})& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{20}p-\frac{1}{2}q-\frac{1}{2}.\frac{3}{20}& \text{Uitwerken } \\ & =pq+\frac{3}{20}p-\frac{1}{2}q-\frac{3}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{10}-x)(\frac{-15}{5}-b)& =(\color{red}{-x}+\color{orange}{\frac{4}{5}}).(\color{green}{-b}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{4}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bx+3x-\frac{4}{5}b-\frac{4}{5}.3& \text{Uitwerken } \\ & =bx+3x-\frac{4}{5}b-\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{20}+p)(\frac{10}{19}+p)& =(\color{red}{p}+\color{orange}{\frac{3}{10}}).(\color{green}{p}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{10}{19}p+\frac{3}{10}p+\frac{3}{10}.\frac{10}{19}& \text{Uitwerken } \\ & =p^2+(\frac{10}{19}+\frac{3}{10})p+\frac{30}{190} & \text{Neem samen} \\ &=p^2+\frac{157}{190}p+\frac{30}{190} & \text{Maak de som} \\ &=p^2+\frac{157}{190}p+\frac{3}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{-18}{19}-x)(x+\frac{-4}{19})& =(\color{red}{-x}+\color{orange}{\frac{-18}{19}}).(\color{green}{x}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{4}{19}x-\frac{18}{19}x+\frac{18}{19}.\frac{4}{19}& \text{Uitwerken } \\ & =-x^2+(\frac{4}{19}+(\frac{-18}{19}))x+(\frac{-72}{361}) & \text{Neem samen} \\ &=-x^2-\frac{14}{19}x+(\frac{-72}{361}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-17}{3}-q)(\frac{19}{20}-x)& =(\color{red}{-q}+\color{orange}{\frac{-17}{3}}).(\color{green}{-x}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{20}q+\frac{17}{3}x-\frac{17}{3}.\frac{19}{20}& \text{Uitwerken } \\ & =qx-\frac{19}{20}q+\frac{17}{3}x-\frac{323}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-14}{3}+a)(\frac{-18}{2}-a)& =(\color{red}{a}+\color{orange}{\frac{-14}{3}}).(\color{green}{-a}+\color{blue}{(-9)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(-9)} + \color{orange}{(\frac{-14}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -aa-9a+\frac{14}{3}a+\frac{14}{3}.9& \text{Uitwerken } \\ & =-a^2+((-9)+\frac{14}{3})a+(\frac{-126}{3}) & \text{Neem samen} \\ &=-a^2-\frac{13}{3}a+(\frac{-126}{3}) & \text{Maak de som} \\ &=-a^2-\frac{13}{3}a+(-42) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{-7}{13}+q)(b-\frac{-4}{13})& =(\color{red}{q}+\color{orange}{\frac{-7}{13}}).(\color{green}{b}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{13}q-\frac{7}{13}b-\frac{7}{13}.\frac{4}{13}& \text{Uitwerken } \\ & =bq+\frac{4}{13}q-\frac{7}{13}b-\frac{28}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-12}{11}-q)(q+\frac{10}{4})& =(\color{red}{-q}+\color{orange}{\frac{-12}{11}}).(\color{green}{q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{5}{2}q-\frac{12}{11}q-\frac{12}{11}.\frac{5}{2}& \text{Uitwerken } \\ & =-q^2+((\frac{-5}{2})+(\frac{-12}{11}))q-\frac{60}{22} & \text{Neem samen} \\ &=-q^2-\frac{79}{22}q-\frac{60}{22} & \text{Maak de som} \\ &=-q^2-\frac{79}{22}q-\frac{30}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(a+\frac{16}{8})(\frac{20}{5}+a)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = aa+4a+2a+2.4& \text{Uitwerken } \\ & =a^2+(4+2)a+8 & \text{Neem samen} \\ &=a^2+6a+8 & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(4+b)(\frac{-18}{6}-q)& =(\color{red}{b}+\color{orange}{4}).(\color{green}{-q}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(4)} . \color{green}{(-q)} + \color{orange}{(4)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bq-3b-4q-4.3& \text{Uitwerken } \\ & =-bq-3b-4q-12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{12}{6}-b)(\frac{-12}{14}-a)& =(\color{red}{-b}+\color{orange}{2}).(\color{green}{-a}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(2)} . \color{green}{(-a)} + \color{orange}{(2)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{6}{7}b-2a-2.\frac{6}{7}& \text{Uitwerken } \\ & =ab+\frac{6}{7}b-2a-\frac{12}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-2}{5})(\frac{-8}{20}+b)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{5}x-\frac{2}{5}b+\frac{2}{5}.\frac{2}{5}& \text{Uitwerken } \\ & =bx-\frac{2}{5}x-\frac{2}{5}b+\frac{4}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-17 08:53:34
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