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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{10}{5}-q)(q-\frac{-8}{14})& =(\color{red}{-q}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{4}{7}q+2q+2.\frac{4}{7}& \text{Uitwerken } \\ & =-q^2+((\frac{-4}{7})+2)q+(\frac{-8}{7}) & \text{Neem samen} \\ &=-q^2+\frac{10}{7}q+(\frac{-8}{7}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{11}{19}-x)(q-\frac{14}{14})& =(\color{red}{-x}+\color{orange}{\frac{11}{19}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{11}{19})} . \color{green}{(q)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1x+\frac{11}{19}q-\frac{11}{19}.1& \text{Uitwerken } \\ & =-qx+1x+\frac{11}{19}q-\frac{11}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{9}{4})(p+\frac{-6}{17})& =(\color{red}{x}+\color{orange}{\frac{9}{4}}).(\color{green}{p}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{6}{17}x+\frac{9}{4}p-\frac{9}{4}.\frac{6}{17}& \text{Uitwerken } \\ & =px-\frac{6}{17}x+\frac{9}{4}p-\frac{54}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{6}{17}x+\frac{9}{4}p-\frac{27}{34} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{14}{6}-p)(q-\frac{-6}{20})& =(\color{red}{-p}+\color{orange}{\frac{7}{3}}).(\color{green}{q}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{10}p+\frac{7}{3}q+\frac{7}{3}.\frac{3}{10}& \text{Uitwerken } \\ & =-pq-\frac{3}{10}p+\frac{7}{3}q+\frac{21}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{3}{10}p+\frac{7}{3}q+\frac{7}{10} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{15}-b)(p+(-20))& =(\color{red}{-b}+\color{orange}{\frac{-16}{15}}).(\color{green}{p}+\color{blue}{(-20)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-20)} + \color{orange}{(\frac{-16}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = -bp+20b-\frac{16}{15}p+\frac{16}{15}.20& \text{Uitwerken } \\ & =-bp+20b-\frac{16}{15}p+\frac{320}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+20b-\frac{16}{15}p+\frac{64}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-15}{15})(\frac{11}{18}+p)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{18}q+1p+1.\frac{11}{18}& \text{Uitwerken } \\ & =pq+\frac{11}{18}q+1p+\frac{11}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{15}-q)(a-\frac{-13}{15})& =(\color{red}{-q}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{\frac{13}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{15})} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{13}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{13}{15}q+\frac{3}{5}a+\frac{3}{5}.\frac{13}{15}& \text{Uitwerken } \\ & =-aq-\frac{13}{15}q+\frac{3}{5}a+\frac{39}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{13}{15}q+\frac{3}{5}a+\frac{13}{25} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{11}{15}-x)(a+\frac{-4}{5})& =(\color{red}{-x}+\color{orange}{\frac{11}{15}}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{11}{15})} . \color{green}{(a)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{4}{5}x+\frac{11}{15}a-\frac{11}{15}.\frac{4}{5}& \text{Uitwerken } \\ & =-ax+\frac{4}{5}x+\frac{11}{15}a-\frac{44}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{10}{19}+p)(p+\frac{13}{18})& =(\color{red}{p}+\color{orange}{\frac{10}{19}}).(\color{green}{p}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{10}{19})} . \color{green}{(p)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{13}{18}p+\frac{10}{19}p+\frac{10}{19}.\frac{13}{18}& \text{Uitwerken } \\ & =p^2+(\frac{13}{18}+\frac{10}{19})p+\frac{130}{342} & \text{Neem samen} \\ &=p^2+\frac{427}{342}p+\frac{130}{342} & \text{Maak de som} \\ &=p^2+\frac{427}{342}p+\frac{65}{171} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-20}{14})(\frac{-18}{2}-q)& =(\color{red}{a}+\color{orange}{\frac{-10}{7}}).(\color{green}{-q}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(-9)} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -aq-9a+\frac{10}{7}q+\frac{10}{7}.9& \text{Uitwerken } \\ & =-aq-9a+\frac{10}{7}q+\frac{90}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-7}{20}+x)(p-\frac{4}{9})& =(\color{red}{x}+\color{orange}{\frac{-7}{20}}).(\color{green}{p}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{9}x-\frac{7}{20}p+\frac{7}{20}.\frac{4}{9}& \text{Uitwerken } \\ & =px-\frac{4}{9}x-\frac{7}{20}p+\frac{28}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{4}{9}x-\frac{7}{20}p+\frac{7}{45} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{15}{19}+p)(q+\frac{-10}{16})& =(\color{red}{p}+\color{orange}{\frac{15}{19}}).(\color{green}{q}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{15}{19})} . \color{green}{(q)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{8}p+\frac{15}{19}q-\frac{15}{19}.\frac{5}{8}& \text{Uitwerken } \\ & =pq-\frac{5}{8}p+\frac{15}{19}q-\frac{75}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-23 17:51:16
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