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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{3}{9})(\frac{5}{12}-x)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{-x}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{5}{12}x-\frac{1}{3}x+\frac{1}{3}.\frac{5}{12}& \text{Uitwerken } \\ & =-x^2+(\frac{5}{12}+(\frac{-1}{3}))x+(\frac{-5}{36}) & \text{Neem samen} \\ &=-x^2+\frac{1}{12}x+(\frac{-5}{36}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-11}{18})(x+\frac{1}{8})& =(\color{red}{a}+\color{orange}{\frac{11}{18}}).(\color{green}{x}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{11}{18})} . \color{green}{(x)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{8}a+\frac{11}{18}x+\frac{11}{18}.\frac{1}{8}& \text{Uitwerken } \\ & =ax+\frac{1}{8}a+\frac{11}{18}x+\frac{11}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{6}{14})(\frac{-14}{6}-a)& =(\color{red}{q}+\color{orange}{\frac{-3}{7}}).(\color{green}{-a}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{7}{3}q+\frac{3}{7}a+\frac{3}{7}.\frac{7}{3}& \text{Uitwerken } \\ & =-aq-\frac{7}{3}q+\frac{3}{7}a+\frac{21}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{7}{3}q+\frac{3}{7}a+1 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{16}{18}+x)(p-\frac{19}{18})& =(\color{red}{x}+\color{orange}{\frac{8}{9}}).(\color{green}{p}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{18}x+\frac{8}{9}p-\frac{8}{9}.\frac{19}{18}& \text{Uitwerken } \\ & =px-\frac{19}{18}x+\frac{8}{9}p-\frac{152}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{19}{18}x+\frac{8}{9}p-\frac{76}{81} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-12}{17})(\frac{9}{11}-a)& =(\color{red}{q}+\color{orange}{\frac{-12}{17}}).(\color{green}{-a}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-12}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{11}q+\frac{12}{17}a-\frac{12}{17}.\frac{9}{11}& \text{Uitwerken } \\ & =-aq+\frac{9}{11}q+\frac{12}{17}a-\frac{108}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{8}{5}-b)(\frac{6}{5}+b)& =(\color{red}{-b}+\color{orange}{\frac{8}{5}}).(\color{green}{b}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{8}{5})} . \color{green}{(b)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{6}{5}b+\frac{8}{5}b+\frac{8}{5}.\frac{6}{5}& \text{Uitwerken } \\ & =-b^2+((\frac{-6}{5})+\frac{8}{5})b+(\frac{-48}{25}) & \text{Neem samen} \\ &=-b^2+\frac{2}{5}b+(\frac{-48}{25}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(a+\frac{-6}{6})(x+\frac{19}{18})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{19}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{19}{18})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{19}{18})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{18}a-1x-1.\frac{19}{18}& \text{Uitwerken } \\ & =ax+\frac{19}{18}a-1x-\frac{19}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{4}-a)(\frac{9}{2}+x)& =(\color{red}{-a}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{9}{2}a+3x+3.\frac{9}{2}& \text{Uitwerken } \\ & =-ax-\frac{9}{2}a+3x+\frac{27}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{14}{3})(b-\frac{-18}{3})& =(\color{red}{q}+\color{orange}{\frac{-14}{3}}).(\color{green}{b}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(6)} + \color{orange}{(\frac{-14}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bq+6q-\frac{14}{3}b-\frac{14}{3}.6& \text{Uitwerken } \\ & =bq+6q-\frac{14}{3}b-\frac{84}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+6q-\frac{14}{3}b-28 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-4}{12}-a)(a-\frac{-9}{16})& =(\color{red}{-a}+\color{orange}{\frac{-1}{3}}).(\color{green}{a}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{9}{16}a-\frac{1}{3}a-\frac{1}{3}.\frac{9}{16}& \text{Uitwerken } \\ & =-a^2+((\frac{-9}{16})+(\frac{-1}{3}))a-\frac{9}{48} & \text{Neem samen} \\ &=-a^2-\frac{43}{48}a-\frac{9}{48} & \text{Maak de som} \\ &=-a^2-\frac{43}{48}a-\frac{3}{16} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(b-\frac{16}{13})(a+\frac{17}{7})& =(\color{red}{b}+\color{orange}{\frac{-16}{13}}).(\color{green}{a}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{7}b-\frac{16}{13}a-\frac{16}{13}.\frac{17}{7}& \text{Uitwerken } \\ & =ab+\frac{17}{7}b-\frac{16}{13}a-\frac{272}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-14}{18})(\frac{-9}{4}+b)& =(\color{red}{x}+\color{orange}{\frac{7}{9}}).(\color{green}{b}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{7}{9})} . \color{green}{(b)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{4}x+\frac{7}{9}b-\frac{7}{9}.\frac{9}{4}& \text{Uitwerken } \\ & =bx-\frac{9}{4}x+\frac{7}{9}b-\frac{63}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{9}{4}x+\frac{7}{9}b-\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-25 00:22:40
Een site van Busleyden Atheneum Mechelen