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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-6)(\frac{-11}{19}-x)& =(\color{red}{x}+\color{orange}{(-6)}).(\color{green}{-x}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(-6)} . \color{green}{(-x)} + \color{orange}{(-6)} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{11}{19}x+6x+6.\frac{11}{19}& \text{Uitwerken } \\ & =-x^2+((\frac{-11}{19})+6)x+(\frac{-66}{19}) & \text{Neem samen} \\ &=-x^2+\frac{103}{19}x+(\frac{-66}{19}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(x+\frac{9}{6})(p-\frac{-11}{20})& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{20}x+\frac{3}{2}p+\frac{3}{2}.\frac{11}{20}& \text{Uitwerken } \\ & =px+\frac{11}{20}x+\frac{3}{2}p+\frac{33}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{17}{19})(q+\frac{-9}{16})& =(\color{red}{a}+\color{orange}{\frac{17}{19}}).(\color{green}{q}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(\frac{17}{19})} . \color{green}{(q)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{9}{16}a+\frac{17}{19}q-\frac{17}{19}.\frac{9}{16}& \text{Uitwerken } \\ & =aq-\frac{9}{16}a+\frac{17}{19}q-\frac{153}{304} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{7}{12})(p+\frac{1}{6})& =(\color{red}{x}+\color{orange}{\frac{-7}{12}}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{6}x-\frac{7}{12}p-\frac{7}{12}.\frac{1}{6}& \text{Uitwerken } \\ & =px+\frac{1}{6}x-\frac{7}{12}p-\frac{7}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{7}+q)(a+\frac{-17}{14})& =(\color{red}{q}+\color{orange}{\frac{5}{7}}).(\color{green}{a}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{14}q+\frac{5}{7}a-\frac{5}{7}.\frac{17}{14}& \text{Uitwerken } \\ & =aq-\frac{17}{14}q+\frac{5}{7}a-\frac{85}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-16}{11}+x)(\frac{10}{6}+q)& =(\color{red}{x}+\color{orange}{\frac{-16}{11}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{3}x-\frac{16}{11}q-\frac{16}{11}.\frac{5}{3}& \text{Uitwerken } \\ & =qx+\frac{5}{3}x-\frac{16}{11}q-\frac{80}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-20}{5}+b)(\frac{5}{4}-q)& =(\color{red}{b}+\color{orange}{(-4)}).(\color{green}{-q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(-4)} . \color{green}{(-q)} + \color{orange}{(-4)} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{4}b+4q-4.\frac{5}{4}& \text{Uitwerken } \\ & =-bq+\frac{5}{4}b+4q-\frac{20}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{5}{4}b+4q-5 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-16}{8}+b)(\frac{10}{12}-a)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{-a}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(-2)} . \color{green}{(-a)} + \color{orange}{(-2)} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{6}b+2a-2.\frac{5}{6}& \text{Uitwerken } \\ & =-ab+\frac{5}{6}b+2a-\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{6}b+2a-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{9}{2}+p)(\frac{-8}{7}+p)& =(\color{red}{p}+\color{orange}{\frac{9}{2}}).(\color{green}{p}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{9}{2})} . \color{green}{(p)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{8}{7}p+\frac{9}{2}p-\frac{9}{2}.\frac{8}{7}& \text{Uitwerken } \\ & =p^2+((\frac{-8}{7})+\frac{9}{2})p-(\frac{-72}{14}) & \text{Neem samen} \\ &=p^2+\frac{47}{14}p-(\frac{-72}{14}) & \text{Maak de som} \\ &=p^2+\frac{47}{14}p+\frac{36}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(b+\frac{11}{9})(p-\frac{2}{18})& =(\color{red}{b}+\color{orange}{\frac{11}{9}}).(\color{green}{p}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{11}{9})} . \color{green}{(p)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{9}b+\frac{11}{9}p-\frac{11}{9}.\frac{1}{9}& \text{Uitwerken } \\ & =bp-\frac{1}{9}b+\frac{11}{9}p-\frac{11}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{6}{15})(\frac{7}{13}+q)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{13}x-\frac{2}{5}q-\frac{2}{5}.\frac{7}{13}& \text{Uitwerken } \\ & =qx+\frac{7}{13}x-\frac{2}{5}q-\frac{14}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-8}{13}+x)(p-\frac{11}{2})& =(\color{red}{x}+\color{orange}{\frac{-8}{13}}).(\color{green}{p}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{-8}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{13})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{2}x-\frac{8}{13}p+\frac{8}{13}.\frac{11}{2}& \text{Uitwerken } \\ & =px-\frac{11}{2}x-\frac{8}{13}p+\frac{88}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{11}{2}x-\frac{8}{13}p+\frac{44}{13} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-23 21:19:17
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