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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{5}{8}+a)(p+\frac{8}{9})& =(\color{red}{a}+\color{orange}{\frac{5}{8}}).(\color{green}{p}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{5}{8})} . \color{green}{(p)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{9}a+\frac{5}{8}p+\frac{5}{8}.\frac{8}{9}& \text{Uitwerken } \\ & =ap+\frac{8}{9}a+\frac{5}{8}p+\frac{40}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{8}{9}a+\frac{5}{8}p+\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-5}{3})(\frac{2}{20}+a)& =(\color{red}{a}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{10}a+\frac{5}{3}a+\frac{5}{3}.\frac{1}{10}& \text{Uitwerken } \\ & =a^2+(\frac{1}{10}+\frac{5}{3})a+\frac{5}{30} & \text{Neem samen} \\ &=a^2+\frac{53}{30}a+\frac{5}{30} & \text{Maak de som} \\ &=a^2+\frac{53}{30}a+\frac{1}{6} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-16}{10})(\frac{14}{16}-q)& =(\color{red}{p}+\color{orange}{\frac{-8}{5}}).(\color{green}{-q}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{7}{8}p+\frac{8}{5}q-\frac{8}{5}.\frac{7}{8}& \text{Uitwerken } \\ & =-pq+\frac{7}{8}p+\frac{8}{5}q-\frac{56}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{7}{8}p+\frac{8}{5}q-\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b-\frac{13}{13})(a-\frac{-2}{8})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{4}b-1a-1.\frac{1}{4}& \text{Uitwerken } \\ & =ab+\frac{1}{4}b-1a-\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-7}{17})(\frac{-2}{15}+b)& =(\color{red}{q}+\color{orange}{\frac{-7}{17}}).(\color{green}{b}+\color{blue}{\frac{-2}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{15})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{-2}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{15}q-\frac{7}{17}b+\frac{7}{17}.\frac{2}{15}& \text{Uitwerken } \\ & =bq-\frac{2}{15}q-\frac{7}{17}b+\frac{14}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-15}{19})(b-\frac{-13}{5})& =(\color{red}{q}+\color{orange}{\frac{-15}{19}}).(\color{green}{b}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{-15}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{5}q-\frac{15}{19}b-\frac{15}{19}.\frac{13}{5}& \text{Uitwerken } \\ & =bq+\frac{13}{5}q-\frac{15}{19}b-\frac{195}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{13}{5}q-\frac{15}{19}b-\frac{39}{19} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-13}{16}+x)(\frac{1}{12}+a)& =(\color{red}{x}+\color{orange}{\frac{-13}{16}}).(\color{green}{a}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{12}x-\frac{13}{16}a-\frac{13}{16}.\frac{1}{12}& \text{Uitwerken } \\ & =ax+\frac{1}{12}x-\frac{13}{16}a-\frac{13}{192} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{1}{15})(q+\frac{-19}{6})& =(\color{red}{p}+\color{orange}{\frac{-1}{15}}).(\color{green}{q}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{6}p-\frac{1}{15}q+\frac{1}{15}.\frac{19}{6}& \text{Uitwerken } \\ & =pq-\frac{19}{6}p-\frac{1}{15}q+\frac{19}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{9}{16}+q)(\frac{-14}{3}+b)& =(\color{red}{q}+\color{orange}{\frac{9}{16}}).(\color{green}{b}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(\frac{9}{16})} . \color{green}{(b)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{14}{3}q+\frac{9}{16}b-\frac{9}{16}.\frac{14}{3}& \text{Uitwerken } \\ & =bq-\frac{14}{3}q+\frac{9}{16}b-\frac{126}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{14}{3}q+\frac{9}{16}b-\frac{21}{8} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x+\frac{9}{6})((-3)+x)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = xx-3x+\frac{3}{2}x-\frac{3}{2}.3& \text{Uitwerken } \\ & =x^2+((-3)+\frac{3}{2})x-(\frac{-9}{2}) & \text{Neem samen} \\ &=x^2-\frac{3}{2}x-(\frac{-9}{2}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(p+2)(a-\frac{-16}{5})& =(\color{red}{p}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{5}p+2a+2.\frac{16}{5}& \text{Uitwerken } \\ & =ap+\frac{16}{5}p+2a+\frac{32}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-20}{18})(q+\frac{8}{18})& =(\color{red}{x}+\color{orange}{\frac{10}{9}}).(\color{green}{q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{10}{9})} . \color{green}{(q)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{9}x+\frac{10}{9}q+\frac{10}{9}.\frac{4}{9}& \text{Uitwerken } \\ & =qx+\frac{4}{9}x+\frac{10}{9}q+\frac{40}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-01 09:39:37
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