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

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

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Verbetersleutel

  1. \(\begin{align}(\frac{-16}{3}+b)(16+a)& =(\color{red}{b}+\color{orange}{\frac{-16}{3}}).(\color{green}{a}+\color{blue}{16})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(16)} + \color{orange}{(\frac{-16}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = ab+16b-\frac{16}{3}a-\frac{16}{3}.16& \text{Uitwerken } \\ & =ab+16b-\frac{16}{3}a-\frac{256}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-7}{11})(\frac{-3}{3}+p)& =(\color{red}{q}+\color{orange}{\frac{7}{11}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{7}{11})} . \color{green}{(p)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1q+\frac{7}{11}p-\frac{7}{11}.1& \text{Uitwerken } \\ & =pq-1q+\frac{7}{11}p-\frac{7}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-20}{17})(b+\frac{5}{19})& =(\color{red}{b}+\color{orange}{\frac{20}{17}}).(\color{green}{b}+\color{blue}{\frac{5}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{19})} + \color{orange}{(\frac{20}{17})} . \color{green}{(b)} + \color{orange}{(\frac{20}{17})} . \color{blue}{(\frac{5}{19})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{19}b+\frac{20}{17}b+\frac{20}{17}.\frac{5}{19}& \text{Uitwerken } \\ & =b^2+(\frac{5}{19}+\frac{20}{17})b+\frac{100}{323} & \text{Neem samen} \\ &=b^2+\frac{465}{323}b+\frac{100}{323} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-4}{16})(\frac{13}{12}+q)& =(\color{red}{b}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{12}b-\frac{1}{4}q-\frac{1}{4}.\frac{13}{12}& \text{Uitwerken } \\ & =bq+\frac{13}{12}b-\frac{1}{4}q-\frac{13}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-4}{9})(\frac{-18}{19}+b)& =(\color{red}{x}+\color{orange}{\frac{-4}{9}}).(\color{green}{b}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{18}{19}x-\frac{4}{9}b+\frac{4}{9}.\frac{18}{19}& \text{Uitwerken } \\ & =bx-\frac{18}{19}x-\frac{4}{9}b+\frac{72}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{18}{19}x-\frac{4}{9}b+\frac{8}{19} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-15}{6})(p+(-13))& =(\color{red}{p}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{(-13)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-13)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = pp-13p-\frac{5}{2}p+\frac{5}{2}.13& \text{Uitwerken } \\ & =p^2+((-13)+(\frac{-5}{2}))p+\frac{65}{2} & \text{Neem samen} \\ &=p^2-\frac{31}{2}p+\frac{65}{2} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-3}{12})(x+\frac{12}{6})& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = xx+2x+\frac{1}{4}x+\frac{1}{4}.2& \text{Uitwerken } \\ & =x^2+(2+\frac{1}{4})x+\frac{2}{4} & \text{Neem samen} \\ &=x^2+\frac{9}{4}x+\frac{2}{4} & \text{Maak de som} \\ &=x^2+\frac{9}{4}x+\frac{1}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{6}{12}+a)(\frac{8}{14}+a)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{4}{7}a+\frac{1}{2}a+\frac{1}{2}.\frac{4}{7}& \text{Uitwerken } \\ & =a^2+(\frac{4}{7}+\frac{1}{2})a+\frac{4}{14} & \text{Neem samen} \\ &=a^2+\frac{15}{14}a+\frac{4}{14} & \text{Maak de som} \\ &=a^2+\frac{15}{14}a+\frac{2}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-18}{5})(\frac{12}{13}+x)& =(\color{red}{x}+\color{orange}{\frac{18}{5}}).(\color{green}{x}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{18}{5})} . \color{green}{(x)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{12}{13}x+\frac{18}{5}x+\frac{18}{5}.\frac{12}{13}& \text{Uitwerken } \\ & =x^2+(\frac{12}{13}+\frac{18}{5})x+\frac{216}{65} & \text{Neem samen} \\ &=x^2+\frac{294}{65}x+\frac{216}{65} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{17}{6}-x)(\frac{5}{19}-x)& =(\color{red}{-x}+\color{orange}{\frac{17}{6}}).(\color{green}{-x}+\color{blue}{\frac{5}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{19})} + \color{orange}{(\frac{17}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{5}{19})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{5}{19}x-\frac{17}{6}x+\frac{17}{6}.\frac{5}{19}& \text{Uitwerken } \\ & =x^2+((\frac{-5}{19})+(\frac{-17}{6}))x+\frac{85}{114} & \text{Neem samen} \\ &=x^2-\frac{353}{114}x+\frac{85}{114} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-17}{12})(\frac{-20}{3}-a)& =(\color{red}{q}+\color{orange}{\frac{-17}{12}}).(\color{green}{-a}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{20}{3}q+\frac{17}{12}a+\frac{17}{12}.\frac{20}{3}& \text{Uitwerken } \\ & =-aq-\frac{20}{3}q+\frac{17}{12}a+\frac{340}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{20}{3}q+\frac{17}{12}a+\frac{85}{9} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a-\frac{5}{4})(\frac{3}{6}+q)& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{2}a-\frac{5}{4}q-\frac{5}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =aq+\frac{1}{2}a-\frac{5}{4}q-\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-31 21:46:16
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