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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{6}{11}-b)(\frac{14}{17}+p)& =(\color{red}{-b}+\color{orange}{\frac{6}{11}}).(\color{green}{p}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{6}{11})} . \color{green}{(p)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{14}{17}b+\frac{6}{11}p+\frac{6}{11}.\frac{14}{17}& \text{Uitwerken } \\ & =-bp-\frac{14}{17}b+\frac{6}{11}p+\frac{84}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{15}{13})(\frac{13}{2}-x)& =(\color{red}{a}+\color{orange}{\frac{-15}{13}}).(\color{green}{-x}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{2}a+\frac{15}{13}x-\frac{15}{13}.\frac{13}{2}& \text{Uitwerken } \\ & =-ax+\frac{13}{2}a+\frac{15}{13}x-\frac{195}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{13}{2}a+\frac{15}{13}x-\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{15}{20})(q-\frac{11}{12})& =(\color{red}{q}+\color{orange}{\frac{3}{4}}).(\color{green}{q}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{12}q+\frac{3}{4}q-\frac{3}{4}.\frac{11}{12}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{12})+\frac{3}{4})q-(\frac{-33}{48}) & \text{Neem samen} \\ &=q^2-\frac{2}{12}q-(\frac{-33}{48}) & \text{Maak de som} \\ &=q^2-\frac{1}{6}q+\frac{11}{16} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(a+\frac{14}{9})(a-\frac{-20}{3})& =(\color{red}{a}+\color{orange}{\frac{14}{9}}).(\color{green}{a}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{14}{9})} . \color{green}{(a)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{20}{3}a+\frac{14}{9}a+\frac{14}{9}.\frac{20}{3}& \text{Uitwerken } \\ & =a^2+(\frac{20}{3}+\frac{14}{9})a+\frac{280}{27} & \text{Neem samen} \\ &=a^2+\frac{74}{9}a+\frac{280}{27} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(q+\frac{18}{14})(p+\frac{11}{3})& =(\color{red}{q}+\color{orange}{\frac{9}{7}}).(\color{green}{p}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{9}{7})} . \color{green}{(p)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{3}q+\frac{9}{7}p+\frac{9}{7}.\frac{11}{3}& \text{Uitwerken } \\ & =pq+\frac{11}{3}q+\frac{9}{7}p+\frac{99}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{11}{3}q+\frac{9}{7}p+\frac{33}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{8}{16}+x)(a+\frac{2}{10})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{5}x+\frac{1}{2}a+\frac{1}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =ax+\frac{1}{5}x+\frac{1}{2}a+\frac{1}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-10}{13})(\frac{7}{19}+b)& =(\color{red}{q}+\color{orange}{\frac{10}{13}}).(\color{green}{b}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{10}{13})} . \color{green}{(b)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{19}q+\frac{10}{13}b+\frac{10}{13}.\frac{7}{19}& \text{Uitwerken } \\ & =bq+\frac{7}{19}q+\frac{10}{13}b+\frac{70}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{9}{2}-q)(\frac{16}{18}+b)& =(\color{red}{-q}+\color{orange}{\frac{9}{2}}).(\color{green}{b}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{9}{2})} . \color{green}{(b)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{8}{9}q+\frac{9}{2}b+\frac{9}{2}.\frac{8}{9}& \text{Uitwerken } \\ & =-bq-\frac{8}{9}q+\frac{9}{2}b+\frac{72}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{8}{9}q+\frac{9}{2}b+4 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{13}{10})(x+\frac{-16}{13})& =(\color{red}{x}+\color{orange}{\frac{-13}{10}}).(\color{green}{x}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{16}{13}x-\frac{13}{10}x+\frac{13}{10}.\frac{16}{13}& \text{Uitwerken } \\ & =x^2+((\frac{-16}{13})+(\frac{-13}{10}))x+\frac{208}{130} & \text{Neem samen} \\ &=x^2-\frac{329}{130}x+\frac{208}{130} & \text{Maak de som} \\ &=x^2-\frac{329}{130}x+\frac{8}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(q+\frac{15}{5})(\frac{-10}{7}+p)& =(\color{red}{q}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{10}{7}q+3p-3.\frac{10}{7}& \text{Uitwerken } \\ & =pq-\frac{10}{7}q+3p-\frac{30}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-10)(\frac{11}{11}-x)& =(\color{red}{b}+\color{orange}{(-10)}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(-10)} . \color{green}{(-x)} + \color{orange}{(-10)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1b+10x-10.1& \text{Uitwerken } \\ & =-bx+1b+10x-10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{8}{11})(q+\frac{-2}{11})& =(\color{red}{b}+\color{orange}{\frac{8}{11}}).(\color{green}{q}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{8}{11})} . \color{green}{(q)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{11}b+\frac{8}{11}q-\frac{8}{11}.\frac{2}{11}& \text{Uitwerken } \\ & =bq-\frac{2}{11}b+\frac{8}{11}q-\frac{16}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-04 08:48:50
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