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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{3}{3})(p+\frac{-19}{17})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{17}x+1p-1.\frac{19}{17}& \text{Uitwerken } \\ & =px-\frac{19}{17}x+1p-\frac{19}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{15}{12}+q)(q+\frac{-6}{14})& =(\color{red}{q}+\color{orange}{\frac{5}{4}}).(\color{green}{q}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{3}{7}q+\frac{5}{4}q-\frac{5}{4}.\frac{3}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-3}{7})+\frac{5}{4})q-(\frac{-15}{28}) & \text{Neem samen} \\ &=q^2+\frac{23}{28}q-(\frac{-15}{28}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(b-\frac{19}{5})(\frac{-15}{4}-b)& =(\color{red}{b}+\color{orange}{\frac{-19}{5}}).(\color{green}{-b}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{15}{4}b+\frac{19}{5}b+\frac{19}{5}.\frac{15}{4}& \text{Uitwerken } \\ & =-b^2+((\frac{-15}{4})+\frac{19}{5})b+(\frac{-285}{20}) & \text{Neem samen} \\ &=-b^2+\frac{1}{20}b+(\frac{-285}{20}) & \text{Maak de som} \\ &=-b^2+\frac{1}{20}b+(\frac{-57}{4}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(q-\frac{19}{16})(a-\frac{-15}{10})& =(\color{red}{q}+\color{orange}{\frac{-19}{16}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{2}q-\frac{19}{16}a-\frac{19}{16}.\frac{3}{2}& \text{Uitwerken } \\ & =aq+\frac{3}{2}q-\frac{19}{16}a-\frac{57}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(5+a)(\frac{-20}{13}-x)& =(\color{red}{a}+\color{orange}{5}).(\color{green}{-x}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(5)} . \color{green}{(-x)} + \color{orange}{(5)} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{20}{13}a-5x-5.\frac{20}{13}& \text{Uitwerken } \\ & =-ax-\frac{20}{13}a-5x-\frac{100}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{15}{4})(\frac{3}{6}-x)& =(\color{red}{b}+\color{orange}{\frac{-15}{4}}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{2}b+\frac{15}{4}x-\frac{15}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =-bx+\frac{1}{2}b+\frac{15}{4}x-\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(7-a)(b+\frac{-20}{7})& =(\color{red}{-a}+\color{orange}{7}).(\color{green}{b}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(7)} . \color{green}{(b)} + \color{orange}{(7)} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{20}{7}a+7b-7.\frac{20}{7}& \text{Uitwerken } \\ & =-ab+\frac{20}{7}a+7b-\frac{140}{7} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{20}{7}a+7b-20 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{16}{10})(q-\frac{-14}{3})& =(\color{red}{b}+\color{orange}{\frac{8}{5}}).(\color{green}{q}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{8}{5})} . \color{green}{(q)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{14}{3}b+\frac{8}{5}q+\frac{8}{5}.\frac{14}{3}& \text{Uitwerken } \\ & =bq+\frac{14}{3}b+\frac{8}{5}q+\frac{112}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{19}{2})(\frac{18}{13}+a)& =(\color{red}{p}+\color{orange}{\frac{-19}{2}}).(\color{green}{a}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{18}{13}p-\frac{19}{2}a-\frac{19}{2}.\frac{18}{13}& \text{Uitwerken } \\ & =ap+\frac{18}{13}p-\frac{19}{2}a-\frac{342}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{18}{13}p-\frac{19}{2}a-\frac{171}{13} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{9}+b)(\frac{-20}{14}-b)& =(\color{red}{b}+\color{orange}{\frac{1}{3}}).(\color{green}{-b}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{10}{7}b-\frac{1}{3}b-\frac{1}{3}.\frac{10}{7}& \text{Uitwerken } \\ & =-b^2+((\frac{-10}{7})+(\frac{-1}{3}))b-\frac{10}{21} & \text{Neem samen} \\ &=-b^2-\frac{37}{21}b-\frac{10}{21} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{15}{6}+q)(\frac{-18}{20}+a)& =(\color{red}{q}+\color{orange}{\frac{5}{2}}).(\color{green}{a}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{9}{10}q+\frac{5}{2}a-\frac{5}{2}.\frac{9}{10}& \text{Uitwerken } \\ & =aq-\frac{9}{10}q+\frac{5}{2}a-\frac{45}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{9}{10}q+\frac{5}{2}a-\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-6}{18}-q)(\frac{12}{19}-x)& =(\color{red}{-q}+\color{orange}{\frac{-1}{3}}).(\color{green}{-x}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{12}{19}q+\frac{1}{3}x-\frac{1}{3}.\frac{12}{19}& \text{Uitwerken } \\ & =qx-\frac{12}{19}q+\frac{1}{3}x-\frac{12}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{12}{19}q+\frac{1}{3}x-\frac{4}{19} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-21 20:37:51
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