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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{20}{20})(\frac{13}{16}-b)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{13}{16}q-1b+1.\frac{13}{16}& \text{Uitwerken } \\ & =-bq+\frac{13}{16}q-1b+\frac{13}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-1}{12})(q-\frac{-14}{10})& =(\color{red}{a}+\color{orange}{\frac{1}{12}}).(\color{green}{q}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{1}{12})} . \color{green}{(q)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{5}a+\frac{1}{12}q+\frac{1}{12}.\frac{7}{5}& \text{Uitwerken } \\ & =aq+\frac{7}{5}a+\frac{1}{12}q+\frac{7}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{13}+x)(\frac{-13}{18}-q)& =(\color{red}{x}+\color{orange}{\frac{-16}{13}}).(\color{green}{-q}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{18}x+\frac{16}{13}q+\frac{16}{13}.\frac{13}{18}& \text{Uitwerken } \\ & =-qx-\frac{13}{18}x+\frac{16}{13}q+\frac{208}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{13}{18}x+\frac{16}{13}q+\frac{8}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-5}{11})(p+\frac{7}{17})& =(\color{red}{a}+\color{orange}{\frac{-5}{11}}).(\color{green}{p}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{17}a-\frac{5}{11}p-\frac{5}{11}.\frac{7}{17}& \text{Uitwerken } \\ & =ap+\frac{7}{17}a-\frac{5}{11}p-\frac{35}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{1}{12}+p)(\frac{-9}{3}-a)& =(\color{red}{p}+\color{orange}{\frac{1}{12}}).(\color{green}{-a}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{1}{12})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -ap-3p-\frac{1}{12}a-\frac{1}{12}.3& \text{Uitwerken } \\ & =-ap-3p-\frac{1}{12}a-\frac{3}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-3p-\frac{1}{12}a-\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+\frac{17}{6})(\frac{-2}{9}-b)& =(\color{red}{q}+\color{orange}{\frac{17}{6}}).(\color{green}{-b}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{17}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{2}{9}q-\frac{17}{6}b-\frac{17}{6}.\frac{2}{9}& \text{Uitwerken } \\ & =-bq-\frac{2}{9}q-\frac{17}{6}b-\frac{34}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{2}{9}q-\frac{17}{6}b-\frac{17}{27} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{16}{6}-a)(b+\frac{-13}{13})& =(\color{red}{-a}+\color{orange}{\frac{8}{3}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(-1)} + \color{orange}{(\frac{8}{3})} . \color{green}{(b)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ab+1a+\frac{8}{3}b-\frac{8}{3}.1& \text{Uitwerken } \\ & =-ab+1a+\frac{8}{3}b-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-14}{4}-a)(q-\frac{-3}{2})& =(\color{red}{-a}+\color{orange}{\frac{-7}{2}}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{2}a-\frac{7}{2}q-\frac{7}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =-aq-\frac{3}{2}a-\frac{7}{2}q-\frac{21}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{2}{5})(\frac{9}{18}+p)& =(\color{red}{q}+\color{orange}{\frac{2}{5}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{2}q+\frac{2}{5}p+\frac{2}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =pq+\frac{1}{2}q+\frac{2}{5}p+\frac{2}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{2}q+\frac{2}{5}p+\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-10}{16}-q)(b-\frac{-9}{5})& =(\color{red}{-q}+\color{orange}{\frac{-5}{8}}).(\color{green}{b}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{5}q-\frac{5}{8}b-\frac{5}{8}.\frac{9}{5}& \text{Uitwerken } \\ & =-bq-\frac{9}{5}q-\frac{5}{8}b-\frac{45}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{9}{5}q-\frac{5}{8}b-\frac{9}{8} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-2}{20})(x-\frac{5}{16})& =(\color{red}{x}+\color{orange}{\frac{-1}{10}}).(\color{green}{x}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{5}{16}x-\frac{1}{10}x+\frac{1}{10}.\frac{5}{16}& \text{Uitwerken } \\ & =x^2+((\frac{-5}{16})+(\frac{-1}{10}))x+\frac{5}{160} & \text{Neem samen} \\ &=x^2-\frac{33}{80}x+\frac{5}{160} & \text{Maak de som} \\ &=x^2-\frac{33}{80}x+\frac{1}{32} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{14}-b)(b+\frac{19}{4})& =(\color{red}{-b}+\color{orange}{\frac{4}{7}}).(\color{green}{b}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{4}{7})} . \color{green}{(b)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{19}{4}b+\frac{4}{7}b+\frac{4}{7}.\frac{19}{4}& \text{Uitwerken } \\ & =-b^2+((\frac{-19}{4})+\frac{4}{7})b+(\frac{-76}{28}) & \text{Neem samen} \\ &=-b^2-\frac{117}{28}b+(\frac{-76}{28}) & \text{Maak de som} \\ &=-b^2-\frac{117}{28}b+(\frac{-19}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-06 20:39:18
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