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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{13}{18}+a)(\frac{-11}{6}+q)& =(\color{red}{a}+\color{orange}{\frac{13}{18}}).(\color{green}{q}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{13}{18})} . \color{green}{(q)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{6}a+\frac{13}{18}q-\frac{13}{18}.\frac{11}{6}& \text{Uitwerken } \\ & =aq-\frac{11}{6}a+\frac{13}{18}q-\frac{143}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{-12}{9})(x+\frac{-18}{10})& =(\color{red}{x}+\color{orange}{\frac{-4}{3}}).(\color{green}{x}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{9}{5}x-\frac{4}{3}x+\frac{4}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-9}{5})+(\frac{-4}{3}))x+\frac{36}{15} & \text{Neem samen} \\ &=x^2-\frac{47}{15}x+\frac{36}{15} & \text{Maak de som} \\ &=x^2-\frac{47}{15}x+\frac{12}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{20}-p)(\frac{-16}{8}-b)& =(\color{red}{-p}+\color{orange}{\frac{-11}{20}}).(\color{green}{-b}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-11}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bp+2p+\frac{11}{20}b+\frac{11}{20}.2& \text{Uitwerken } \\ & =bp+2p+\frac{11}{20}b+\frac{22}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+2p+\frac{11}{20}b+\frac{11}{10} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a+\frac{6}{19})(\frac{-19}{11}-b)& =(\color{red}{a}+\color{orange}{\frac{6}{19}}).(\color{green}{-b}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{6}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{19}{11}a-\frac{6}{19}b-\frac{6}{19}.\frac{19}{11}& \text{Uitwerken } \\ & =-ab-\frac{19}{11}a-\frac{6}{19}b-\frac{114}{209} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{19}{11}a-\frac{6}{19}b-\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+(-6))(\frac{16}{13}+x)& =(\color{red}{a}+\color{orange}{(-6)}).(\color{green}{x}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(-6)} . \color{green}{(x)} + \color{orange}{(-6)} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{16}{13}a-6x-6.\frac{16}{13}& \text{Uitwerken } \\ & =ax+\frac{16}{13}a-6x-\frac{96}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{7}{11}+q)(q-\frac{5}{9})& =(\color{red}{q}+\color{orange}{\frac{7}{11}}).(\color{green}{q}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{7}{11})} . \color{green}{(q)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{5}{9}q+\frac{7}{11}q-\frac{7}{11}.\frac{5}{9}& \text{Uitwerken } \\ & =q^2+((\frac{-5}{9})+\frac{7}{11})q-(\frac{-35}{99}) & \text{Neem samen} \\ &=q^2+\frac{8}{99}q-(\frac{-35}{99}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{20}{16}-q)(\frac{10}{6}+p)& =(\color{red}{-q}+\color{orange}{\frac{5}{4}}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{3}q+\frac{5}{4}p+\frac{5}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =-pq-\frac{5}{3}q+\frac{5}{4}p+\frac{25}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-20}{11}+x)(\frac{-19}{3}-q)& =(\color{red}{x}+\color{orange}{\frac{-20}{11}}).(\color{green}{-q}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{3}x+\frac{20}{11}q+\frac{20}{11}.\frac{19}{3}& \text{Uitwerken } \\ & =-qx-\frac{19}{3}x+\frac{20}{11}q+\frac{380}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{20}{14}-a)(p-\frac{16}{5})& =(\color{red}{-a}+\color{orange}{\frac{10}{7}}).(\color{green}{p}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{10}{7})} . \color{green}{(p)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{16}{5}a+\frac{10}{7}p-\frac{10}{7}.\frac{16}{5}& \text{Uitwerken } \\ & =-ap+\frac{16}{5}a+\frac{10}{7}p-\frac{160}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{16}{5}a+\frac{10}{7}p-\frac{32}{7} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x+\frac{-12}{10})(\frac{-10}{7}-a)& =(\color{red}{x}+\color{orange}{\frac{-6}{5}}).(\color{green}{-a}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{10}{7}x+\frac{6}{5}a+\frac{6}{5}.\frac{10}{7}& \text{Uitwerken } \\ & =-ax-\frac{10}{7}x+\frac{6}{5}a+\frac{60}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{10}{7}x+\frac{6}{5}a+\frac{12}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{20}{8}+q)(p-\frac{10}{10})& =(\color{red}{q}+\color{orange}{\frac{5}{2}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1q+\frac{5}{2}p-\frac{5}{2}.1& \text{Uitwerken } \\ & =pq-1q+\frac{5}{2}p-\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{17}{20}-x)(\frac{-7}{6}-q)& =(\color{red}{-x}+\color{orange}{\frac{17}{20}}).(\color{green}{-q}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{17}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{6}x-\frac{17}{20}q-\frac{17}{20}.\frac{7}{6}& \text{Uitwerken } \\ & =qx+\frac{7}{6}x-\frac{17}{20}q-\frac{119}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-05 05:04:23
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