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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-1}{9})(p+\frac{16}{17})& =(\color{red}{b}+\color{orange}{\frac{-1}{9}}).(\color{green}{p}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{16}{17}b-\frac{1}{9}p-\frac{1}{9}.\frac{16}{17}& \text{Uitwerken } \\ & =bp+\frac{16}{17}b-\frac{1}{9}p-\frac{16}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{14}+q)(q+\frac{18}{16})& =(\color{red}{q}+\color{orange}{\frac{-6}{7}}).(\color{green}{q}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{9}{8}q-\frac{6}{7}q-\frac{6}{7}.\frac{9}{8}& \text{Uitwerken } \\ & =q^2+(\frac{9}{8}+(\frac{-6}{7}))q-(\frac{-54}{56}) & \text{Neem samen} \\ &=q^2+\frac{15}{56}q-(\frac{-54}{56}) & \text{Maak de som} \\ &=q^2+\frac{15}{56}q+\frac{27}{28} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{-6}{13}+a)((-3)+x)& =(\color{red}{a}+\color{orange}{\frac{-6}{13}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{-6}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ax-3a-\frac{6}{13}x+\frac{6}{13}.3& \text{Uitwerken } \\ & =ax-3a-\frac{6}{13}x+\frac{18}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-4}{14}+b)(\frac{-2}{12}+a)& =(\color{red}{b}+\color{orange}{\frac{-2}{7}}).(\color{green}{a}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{6}b-\frac{2}{7}a+\frac{2}{7}.\frac{1}{6}& \text{Uitwerken } \\ & =ab-\frac{1}{6}b-\frac{2}{7}a+\frac{2}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{6}b-\frac{2}{7}a+\frac{1}{21} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{4}-b)(\frac{15}{2}-q)& =(\color{red}{-b}+\color{orange}{\frac{-9}{4}}).(\color{green}{-q}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{15}{2}b+\frac{9}{4}q-\frac{9}{4}.\frac{15}{2}& \text{Uitwerken } \\ & =bq-\frac{15}{2}b+\frac{9}{4}q-\frac{135}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}((-16)-x)(\frac{-9}{4}-a)& =(\color{red}{-x}+\color{orange}{(-16)}).(\color{green}{-a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(-16)} . \color{green}{(-a)} + \color{orange}{(-16)} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{4}x+16a+16.\frac{9}{4}& \text{Uitwerken } \\ & =ax+\frac{9}{4}x+16a+\frac{144}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{9}{4}x+16a+36 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{16}{15}-x)(\frac{-5}{17}+p)& =(\color{red}{-x}+\color{orange}{\frac{16}{15}}).(\color{green}{p}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{16}{15})} . \color{green}{(p)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{5}{17}x+\frac{16}{15}p-\frac{16}{15}.\frac{5}{17}& \text{Uitwerken } \\ & =-px+\frac{5}{17}x+\frac{16}{15}p-\frac{80}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{5}{17}x+\frac{16}{15}p-\frac{16}{51} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}((-18)+p)(\frac{7}{20}-p)& =(\color{red}{p}+\color{orange}{(-18)}).(\color{green}{-p}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(-18)} . \color{green}{(-p)} + \color{orange}{(-18)} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{7}{20}p+18p-18.\frac{7}{20}& \text{Uitwerken } \\ & =-p^2+(\frac{7}{20}+18)p-\frac{126}{20} & \text{Neem samen} \\ &=-p^2+\frac{367}{20}p-\frac{126}{20} & \text{Maak de som} \\ &=-p^2+\frac{367}{20}p-\frac{63}{10} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-11}{7}-a)(\frac{4}{6}-p)& =(\color{red}{-a}+\color{orange}{\frac{-11}{7}}).(\color{green}{-p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-11}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{3}a+\frac{11}{7}p-\frac{11}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =ap-\frac{2}{3}a+\frac{11}{7}p-\frac{22}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{4}{6}-x)(x-\frac{-19}{12})& =(\color{red}{-x}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{19}{12}x+\frac{2}{3}x+\frac{2}{3}.\frac{19}{12}& \text{Uitwerken } \\ & =-x^2+((\frac{-19}{12})+\frac{2}{3})x+(\frac{-38}{36}) & \text{Neem samen} \\ &=-x^2-\frac{11}{12}x+(\frac{-38}{36}) & \text{Maak de som} \\ &=-x^2-\frac{11}{12}x+(\frac{-19}{18}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{11}{2}+a)(a+\frac{-16}{10})& =(\color{red}{a}+\color{orange}{\frac{11}{2}}).(\color{green}{a}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{11}{2})} . \color{green}{(a)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{8}{5}a+\frac{11}{2}a-\frac{11}{2}.\frac{8}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-8}{5})+\frac{11}{2})a-(\frac{-88}{10}) & \text{Neem samen} \\ &=a^2+\frac{39}{10}a-(\frac{-88}{10}) & \text{Maak de som} \\ &=a^2+\frac{39}{10}a+\frac{44}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-12}{17})(\frac{-16}{5}+p)& =(\color{red}{x}+\color{orange}{\frac{12}{17}}).(\color{green}{p}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{12}{17})} . \color{green}{(p)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{16}{5}x+\frac{12}{17}p-\frac{12}{17}.\frac{16}{5}& \text{Uitwerken } \\ & =px-\frac{16}{5}x+\frac{12}{17}p-\frac{192}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-14 04:21:11
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