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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{5}{18}-a)(\frac{15}{6}+p)& =(\color{red}{-a}+\color{orange}{\frac{5}{18}}).(\color{green}{p}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{5}{18})} . \color{green}{(p)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{2}a+\frac{5}{18}p+\frac{5}{18}.\frac{5}{2}& \text{Uitwerken } \\ & =-ap-\frac{5}{2}a+\frac{5}{18}p+\frac{25}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-10}{3}-b)(a-\frac{-18}{20})& =(\color{red}{-b}+\color{orange}{\frac{-10}{3}}).(\color{green}{a}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{9}{10}b-\frac{10}{3}a-\frac{10}{3}.\frac{9}{10}& \text{Uitwerken } \\ & =-ab-\frac{9}{10}b-\frac{10}{3}a-\frac{90}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{9}{10}b-\frac{10}{3}a-3 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{10}+p)(\frac{-11}{19}-a)& =(\color{red}{p}+\color{orange}{\frac{3}{5}}).(\color{green}{-a}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{11}{19}p-\frac{3}{5}a-\frac{3}{5}.\frac{11}{19}& \text{Uitwerken } \\ & =-ap-\frac{11}{19}p-\frac{3}{5}a-\frac{33}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-17}{7}-p)(p-\frac{-13}{9})& =(\color{red}{-p}+\color{orange}{\frac{-17}{7}}).(\color{green}{p}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-17}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{7})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{13}{9}p-\frac{17}{7}p-\frac{17}{7}.\frac{13}{9}& \text{Uitwerken } \\ & =-p^2+((\frac{-13}{9})+(\frac{-17}{7}))p-\frac{221}{63} & \text{Neem samen} \\ &=-p^2-\frac{244}{63}p-\frac{221}{63} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a+\frac{11}{11})(\frac{6}{4}-x)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{2}a-1x+1.\frac{3}{2}& \text{Uitwerken } \\ & =-ax+\frac{3}{2}a-1x+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{6}{12})(\frac{-14}{12}+q)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{6}p-\frac{1}{2}q+\frac{1}{2}.\frac{7}{6}& \text{Uitwerken } \\ & =pq-\frac{7}{6}p-\frac{1}{2}q+\frac{7}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{2}{14})(\frac{-13}{13}+b)& =(\color{red}{x}+\color{orange}{\frac{1}{7}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx-1x+\frac{1}{7}b-\frac{1}{7}.1& \text{Uitwerken } \\ & =bx-1x+\frac{1}{7}b-\frac{1}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-5}{13}+b)(\frac{-17}{12}-a)& =(\color{red}{b}+\color{orange}{\frac{-5}{13}}).(\color{green}{-a}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{17}{12}b+\frac{5}{13}a+\frac{5}{13}.\frac{17}{12}& \text{Uitwerken } \\ & =-ab-\frac{17}{12}b+\frac{5}{13}a+\frac{85}{156} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-2}{5})(x-\frac{-2}{18})& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{x}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{9}p-\frac{2}{5}x-\frac{2}{5}.\frac{1}{9}& \text{Uitwerken } \\ & =px+\frac{1}{9}p-\frac{2}{5}x-\frac{2}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-11}{15}-q)(a+\frac{19}{2})& =(\color{red}{-q}+\color{orange}{\frac{-11}{15}}).(\color{green}{a}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{2}q-\frac{11}{15}a-\frac{11}{15}.\frac{19}{2}& \text{Uitwerken } \\ & =-aq-\frac{19}{2}q-\frac{11}{15}a-\frac{209}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-10}{18}-p)(q+\frac{-9}{11})& =(\color{red}{-p}+\color{orange}{\frac{-5}{9}}).(\color{green}{q}+\color{blue}{\frac{-9}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{11})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-9}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{11}p-\frac{5}{9}q+\frac{5}{9}.\frac{9}{11}& \text{Uitwerken } \\ & =-pq+\frac{9}{11}p-\frac{5}{9}q+\frac{45}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{9}{11}p-\frac{5}{9}q+\frac{5}{11} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-18)(\frac{-3}{20}-p)& =(\color{red}{b}+\color{orange}{(-18)}).(\color{green}{-p}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(-18)} . \color{green}{(-p)} + \color{orange}{(-18)} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{20}b+18p+18.\frac{3}{20}& \text{Uitwerken } \\ & =-bp-\frac{3}{20}b+18p+\frac{54}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{3}{20}b+18p+\frac{27}{10} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-19 23:15:26
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