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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-8}{17})(q+\frac{-17}{10})& =(\color{red}{p}+\color{orange}{\frac{8}{17}}).(\color{green}{q}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{8}{17})} . \color{green}{(q)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{10}p+\frac{8}{17}q-\frac{8}{17}.\frac{17}{10}& \text{Uitwerken } \\ & =pq-\frac{17}{10}p+\frac{8}{17}q-\frac{136}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{17}{10}p+\frac{8}{17}q-\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-19}{2}+q)(\frac{18}{10}+x)& =(\color{red}{q}+\color{orange}{\frac{-19}{2}}).(\color{green}{x}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{5}q-\frac{19}{2}x-\frac{19}{2}.\frac{9}{5}& \text{Uitwerken } \\ & =qx+\frac{9}{5}q-\frac{19}{2}x-\frac{171}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+13)(\frac{-17}{17}-a)& =(\color{red}{a}+\color{orange}{13}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(13)} . \color{green}{(-a)} + \color{orange}{(13)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aa-1a-13a-13.1& \text{Uitwerken } \\ & =-a^2+((-1)+(-13))a-13 & \text{Neem samen} \\ &=-a^2-14a-13 & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-7}{2})(\frac{-16}{16}+p)& =(\color{red}{p}+\color{orange}{\frac{-7}{2}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-7}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pp-1p-\frac{7}{2}p+\frac{7}{2}.1& \text{Uitwerken } \\ & =p^2+((-1)+(\frac{-7}{2}))p+\frac{7}{2} & \text{Neem samen} \\ &=p^2-\frac{9}{2}p+\frac{7}{2} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-8}{17}-x)(q-\frac{-16}{15})& =(\color{red}{-x}+\color{orange}{\frac{-8}{17}}).(\color{green}{q}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{16}{15}x-\frac{8}{17}q-\frac{8}{17}.\frac{16}{15}& \text{Uitwerken } \\ & =-qx-\frac{16}{15}x-\frac{8}{17}q-\frac{128}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{1}{14})(x-\frac{12}{5})& =(\color{red}{x}+\color{orange}{\frac{1}{14}}).(\color{green}{x}+\color{blue}{\frac{-12}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{5})} + \color{orange}{(\frac{1}{14})} . \color{green}{(x)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-12}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{12}{5}x+\frac{1}{14}x-\frac{1}{14}.\frac{12}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-12}{5})+\frac{1}{14})x-(\frac{-12}{70}) & \text{Neem samen} \\ &=x^2-\frac{163}{70}x-(\frac{-12}{70}) & \text{Maak de som} \\ &=x^2-\frac{163}{70}x+\frac{6}{35} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{-1}{8}+q)((-20)-p)& =(\color{red}{q}+\color{orange}{\frac{-1}{8}}).(\color{green}{-p}+\color{blue}{(-20)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(-20)} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = -pq-20q+\frac{1}{8}p+\frac{1}{8}.20& \text{Uitwerken } \\ & =-pq-20q+\frac{1}{8}p+\frac{20}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-20q+\frac{1}{8}p+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{19}{20}-a)(b-\frac{-13}{11})& =(\color{red}{-a}+\color{orange}{\frac{19}{20}}).(\color{green}{b}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{19}{20})} . \color{green}{(b)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{13}{11}a+\frac{19}{20}b+\frac{19}{20}.\frac{13}{11}& \text{Uitwerken } \\ & =-ab-\frac{13}{11}a+\frac{19}{20}b+\frac{247}{220} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-16}{12})(x-\frac{-6}{8})& =(\color{red}{a}+\color{orange}{\frac{4}{3}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{4}a+\frac{4}{3}x+\frac{4}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =ax+\frac{3}{4}a+\frac{4}{3}x+\frac{12}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{4}a+\frac{4}{3}x+1 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(13+q)(\frac{-15}{6}+a)& =(\color{red}{q}+\color{orange}{13}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(13)} . \color{green}{(a)} + \color{orange}{(13)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{2}q+13a-13.\frac{5}{2}& \text{Uitwerken } \\ & =aq-\frac{5}{2}q+13a-\frac{65}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{19}-q)(q+\frac{-4}{6})& =(\color{red}{-q}+\color{orange}{\frac{-13}{19}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{2}{3}q-\frac{13}{19}q+\frac{13}{19}.\frac{2}{3}& \text{Uitwerken } \\ & =-q^2+(\frac{2}{3}+(\frac{-13}{19}))q+(\frac{-26}{57}) & \text{Neem samen} \\ &=-q^2-\frac{1}{57}q+(\frac{-26}{57}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{12}+a)(p+\frac{-6}{20})& =(\color{red}{a}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{10}a+\frac{3}{4}p-\frac{3}{4}.\frac{3}{10}& \text{Uitwerken } \\ & =ap-\frac{3}{10}a+\frac{3}{4}p-\frac{9}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-13 07:43:54
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