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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{16}{2}+b)((-10)-p)& =(\color{red}{b}+\color{orange}{8}).(\color{green}{-p}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-10)} + \color{orange}{(8)} . \color{green}{(-p)} + \color{orange}{(8)} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -bp-10b-8p-8.10& \text{Uitwerken } \\ & =-bp-10b-8p-80 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-18}{14}-x)(\frac{-8}{9}-p)& =(\color{red}{-x}+\color{orange}{\frac{-9}{7}}).(\color{green}{-p}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{8}{9}x+\frac{9}{7}p+\frac{9}{7}.\frac{8}{9}& \text{Uitwerken } \\ & =px+\frac{8}{9}x+\frac{9}{7}p+\frac{72}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{8}{9}x+\frac{9}{7}p+\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-1}{11})((-6)+a)& =(\color{red}{b}+\color{orange}{\frac{1}{11}}).(\color{green}{a}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-6)} + \color{orange}{(\frac{1}{11})} . \color{green}{(a)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ab-6b+\frac{1}{11}a-\frac{1}{11}.6& \text{Uitwerken } \\ & =ab-6b+\frac{1}{11}a-\frac{6}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-17}{17}-q)(b-\frac{13}{8})& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{13}{8}q-1b+1.\frac{13}{8}& \text{Uitwerken } \\ & =-bq+\frac{13}{8}q-1b+\frac{13}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{12}-x)(q-\frac{-3}{18})& =(\color{red}{-x}+\color{orange}{\frac{-5}{4}}).(\color{green}{q}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{6}x-\frac{5}{4}q-\frac{5}{4}.\frac{1}{6}& \text{Uitwerken } \\ & =-qx-\frac{1}{6}x-\frac{5}{4}q-\frac{5}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+(-9))(\frac{-9}{7}+q)& =(\color{red}{p}+\color{orange}{(-9)}).(\color{green}{q}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(-9)} . \color{green}{(q)} + \color{orange}{(-9)} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{9}{7}p-9q+9.\frac{9}{7}& \text{Uitwerken } \\ & =pq-\frac{9}{7}p-9q+\frac{81}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-20}{20})(q-\frac{-8}{17})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{8}{17}q-1q-1.\frac{8}{17}& \text{Uitwerken } \\ & =q^2+(\frac{8}{17}+(-1))q-(\frac{-8}{17}) & \text{Neem samen} \\ &=q^2-\frac{9}{17}q-(\frac{-8}{17}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(a+(-3))(b-\frac{-5}{14})& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{14}a-3b-3.\frac{5}{14}& \text{Uitwerken } \\ & =ab+\frac{5}{14}a-3b-\frac{15}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-8}{20}-p)(q+\frac{-8}{15})& =(\color{red}{-p}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{8}{15}p-\frac{2}{5}q+\frac{2}{5}.\frac{8}{15}& \text{Uitwerken } \\ & =-pq+\frac{8}{15}p-\frac{2}{5}q+\frac{16}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-15}{18})(a-\frac{-16}{8})& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq+2q-\frac{5}{6}a-\frac{5}{6}.2& \text{Uitwerken } \\ & =aq+2q-\frac{5}{6}a-\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+2q-\frac{5}{6}a-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{2}{12})(b-\frac{20}{12})& =(\color{red}{x}+\color{orange}{\frac{-1}{6}}).(\color{green}{b}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{3}x-\frac{1}{6}b+\frac{1}{6}.\frac{5}{3}& \text{Uitwerken } \\ & =bx-\frac{5}{3}x-\frac{1}{6}b+\frac{5}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-17}{7})(\frac{-2}{20}+q)& =(\color{red}{p}+\color{orange}{\frac{17}{7}}).(\color{green}{q}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{17}{7})} . \color{green}{(q)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{10}p+\frac{17}{7}q-\frac{17}{7}.\frac{1}{10}& \text{Uitwerken } \\ & =pq-\frac{1}{10}p+\frac{17}{7}q-\frac{17}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-18 12:22:01
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