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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{12}+b)(a-\frac{18}{11})& =(\color{red}{b}+\color{orange}{\frac{5}{4}}).(\color{green}{a}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{18}{11}b+\frac{5}{4}a-\frac{5}{4}.\frac{18}{11}& \text{Uitwerken } \\ & =ab-\frac{18}{11}b+\frac{5}{4}a-\frac{90}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{18}{11}b+\frac{5}{4}a-\frac{45}{22} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p-\frac{11}{15})(\frac{-15}{2}-a)& =(\color{red}{p}+\color{orange}{\frac{-11}{15}}).(\color{green}{-a}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{15}{2}p+\frac{11}{15}a+\frac{11}{15}.\frac{15}{2}& \text{Uitwerken } \\ & =-ap-\frac{15}{2}p+\frac{11}{15}a+\frac{165}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{15}{2}p+\frac{11}{15}a+\frac{11}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p-\frac{16}{12})(\frac{-19}{12}+b)& =(\color{red}{p}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{12}p-\frac{4}{3}b+\frac{4}{3}.\frac{19}{12}& \text{Uitwerken } \\ & =bp-\frac{19}{12}p-\frac{4}{3}b+\frac{76}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{19}{12}p-\frac{4}{3}b+\frac{19}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-12}{18}-p)(q+\frac{-2}{8})& =(\color{red}{-p}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{4}p-\frac{2}{3}q+\frac{2}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =-pq+\frac{1}{4}p-\frac{2}{3}q+\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{1}{4}p-\frac{2}{3}q+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{12}{18}+p)(b+\frac{-7}{19})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{19}p+\frac{2}{3}b-\frac{2}{3}.\frac{7}{19}& \text{Uitwerken } \\ & =bp-\frac{7}{19}p+\frac{2}{3}b-\frac{14}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-9}{14})(\frac{-5}{6}-q)& =(\color{red}{a}+\color{orange}{\frac{9}{14}}).(\color{green}{-q}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{9}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{6}a-\frac{9}{14}q-\frac{9}{14}.\frac{5}{6}& \text{Uitwerken } \\ & =-aq-\frac{5}{6}a-\frac{9}{14}q-\frac{45}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{5}{6}a-\frac{9}{14}q-\frac{15}{28} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x+\frac{10}{20})(q-\frac{-11}{14})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{14}x+\frac{1}{2}q+\frac{1}{2}.\frac{11}{14}& \text{Uitwerken } \\ & =qx+\frac{11}{14}x+\frac{1}{2}q+\frac{11}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-19}{14})(\frac{19}{14}-p)& =(\color{red}{a}+\color{orange}{\frac{-19}{14}}).(\color{green}{-p}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{14}a+\frac{19}{14}p-\frac{19}{14}.\frac{19}{14}& \text{Uitwerken } \\ & =-ap+\frac{19}{14}a+\frac{19}{14}p-\frac{361}{196} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{4}{6})(\frac{1}{9}+q)& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{9}b-\frac{2}{3}q-\frac{2}{3}.\frac{1}{9}& \text{Uitwerken } \\ & =bq+\frac{1}{9}b-\frac{2}{3}q-\frac{2}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-9}{16})(p-\frac{-10}{6})& =(\color{red}{b}+\color{orange}{\frac{9}{16}}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{9}{16})} . \color{green}{(p)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{3}b+\frac{9}{16}p+\frac{9}{16}.\frac{5}{3}& \text{Uitwerken } \\ & =bp+\frac{5}{3}b+\frac{9}{16}p+\frac{45}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{5}{3}b+\frac{9}{16}p+\frac{15}{16} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}((-12)-p)(\frac{6}{14}-q)& =(\color{red}{-p}+\color{orange}{(-12)}).(\color{green}{-q}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(-12)} . \color{green}{(-q)} + \color{orange}{(-12)} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{7}p+12q-12.\frac{3}{7}& \text{Uitwerken } \\ & =pq-\frac{3}{7}p+12q-\frac{36}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{17}{5})(\frac{3}{5}-q)& =(\color{red}{b}+\color{orange}{\frac{17}{5}}).(\color{green}{-q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{17}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{5}b-\frac{17}{5}q+\frac{17}{5}.\frac{3}{5}& \text{Uitwerken } \\ & =-bq+\frac{3}{5}b-\frac{17}{5}q+\frac{51}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-19 19:31:48
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