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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-1}{11})(b-\frac{-8}{13})& =(\color{red}{b}+\color{orange}{\frac{-1}{11}}).(\color{green}{b}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{8}{13}b-\frac{1}{11}b-\frac{1}{11}.\frac{8}{13}& \text{Uitwerken } \\ & =b^2+(\frac{8}{13}+(\frac{-1}{11}))b-(\frac{-8}{143}) & \text{Neem samen} \\ &=b^2+\frac{75}{143}b-(\frac{-8}{143}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(x+\frac{4}{19})(x-\frac{19}{17})& =(\color{red}{x}+\color{orange}{\frac{4}{19}}).(\color{green}{x}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{4}{19})} . \color{green}{(x)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{19}{17}x+\frac{4}{19}x-\frac{4}{19}.\frac{19}{17}& \text{Uitwerken } \\ & =x^2+((\frac{-19}{17})+\frac{4}{19})x-(\frac{-76}{323}) & \text{Neem samen} \\ &=x^2-\frac{293}{323}x-(\frac{-76}{323}) & \text{Maak de som} \\ &=x^2-\frac{293}{323}x+\frac{4}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(p+(-16))(\frac{4}{10}-a)& =(\color{red}{p}+\color{orange}{(-16)}).(\color{green}{-a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(-16)} . \color{green}{(-a)} + \color{orange}{(-16)} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{5}p+16a-16.\frac{2}{5}& \text{Uitwerken } \\ & =-ap+\frac{2}{5}p+16a-\frac{32}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{2}{15})(x+\frac{14}{7})& =(\color{red}{p}+\color{orange}{\frac{2}{15}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{2}{15})} . \color{green}{(x)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = px+2p+\frac{2}{15}x+\frac{2}{15}.2& \text{Uitwerken } \\ & =px+2p+\frac{2}{15}x+\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-15}{2})(\frac{16}{12}+b)& =(\color{red}{b}+\color{orange}{\frac{15}{2}}).(\color{green}{b}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{15}{2})} . \color{green}{(b)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{4}{3}b+\frac{15}{2}b+\frac{15}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =b^2+(\frac{4}{3}+\frac{15}{2})b+\frac{60}{6} & \text{Neem samen} \\ &=b^2+\frac{53}{6}b+\frac{60}{6} & \text{Maak de som} \\ &=b^2+\frac{53}{6}b+10 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(a-\frac{9}{3})(a-\frac{-2}{19})& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{2}{19}a-3a-3.\frac{2}{19}& \text{Uitwerken } \\ & =a^2+(\frac{2}{19}+(-3))a-(\frac{-6}{19}) & \text{Neem samen} \\ &=a^2-\frac{55}{19}a-(\frac{-6}{19}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-19}{3}-q)(b+\frac{11}{20})& =(\color{red}{-q}+\color{orange}{\frac{-19}{3}}).(\color{green}{b}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{11}{20}q-\frac{19}{3}b-\frac{19}{3}.\frac{11}{20}& \text{Uitwerken } \\ & =-bq-\frac{11}{20}q-\frac{19}{3}b-\frac{209}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{4}+q)(\frac{-15}{8}-a)& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{-a}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{15}{8}q+\frac{3}{4}a+\frac{3}{4}.\frac{15}{8}& \text{Uitwerken } \\ & =-aq-\frac{15}{8}q+\frac{3}{4}a+\frac{45}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{10}{14}-p)(\frac{-8}{10}+x)& =(\color{red}{-p}+\color{orange}{\frac{5}{7}}).(\color{green}{x}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{5}{7})} . \color{green}{(x)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{4}{5}p+\frac{5}{7}x-\frac{5}{7}.\frac{4}{5}& \text{Uitwerken } \\ & =-px+\frac{4}{5}p+\frac{5}{7}x-\frac{20}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{4}{5}p+\frac{5}{7}x-\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{11}+q)(\frac{1}{10}+p)& =(\color{red}{q}+\color{orange}{\frac{3}{11}}).(\color{green}{p}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{3}{11})} . \color{green}{(p)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{10}q+\frac{3}{11}p+\frac{3}{11}.\frac{1}{10}& \text{Uitwerken } \\ & =pq+\frac{1}{10}q+\frac{3}{11}p+\frac{3}{110} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-18}{17}+a)(q+\frac{17}{8})& =(\color{red}{a}+\color{orange}{\frac{-18}{17}}).(\color{green}{q}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{8}a-\frac{18}{17}q-\frac{18}{17}.\frac{17}{8}& \text{Uitwerken } \\ & =aq+\frac{17}{8}a-\frac{18}{17}q-\frac{306}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{17}{8}a-\frac{18}{17}q-\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q-\frac{7}{9})(\frac{-15}{6}+p)& =(\color{red}{q}+\color{orange}{\frac{-7}{9}}).(\color{green}{p}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{2}q-\frac{7}{9}p+\frac{7}{9}.\frac{5}{2}& \text{Uitwerken } \\ & =pq-\frac{5}{2}q-\frac{7}{9}p+\frac{35}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-25 16:09:10
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