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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{15}{20})(\frac{10}{18}-a)& =(\color{red}{a}+\color{orange}{\frac{3}{4}}).(\color{green}{-a}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{5}{9}a-\frac{3}{4}a+\frac{3}{4}.\frac{5}{9}& \text{Uitwerken } \\ & =-a^2+(\frac{5}{9}+(\frac{-3}{4}))a+(\frac{-15}{36}) & \text{Neem samen} \\ &=-a^2-\frac{7}{36}a+(\frac{-15}{36}) & \text{Maak de som} \\ &=-a^2-\frac{7}{36}a+(\frac{-5}{12}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{12}{15}+a)(\frac{13}{4}-x)& =(\color{red}{a}+\color{orange}{\frac{4}{5}}).(\color{green}{-x}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{4}a-\frac{4}{5}x+\frac{4}{5}.\frac{13}{4}& \text{Uitwerken } \\ & =-ax+\frac{13}{4}a-\frac{4}{5}x+\frac{52}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{13}{4}a-\frac{4}{5}x+\frac{13}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-6}{6})(q-\frac{19}{17})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{17}p-1q+1.\frac{19}{17}& \text{Uitwerken } \\ & =pq-\frac{19}{17}p-1q+\frac{19}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{13}{8})(b+\frac{-6}{7})& =(\color{red}{b}+\color{orange}{\frac{-13}{8}}).(\color{green}{b}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{6}{7}b-\frac{13}{8}b+\frac{13}{8}.\frac{6}{7}& \text{Uitwerken } \\ & =b^2+((\frac{-6}{7})+(\frac{-13}{8}))b+\frac{78}{56} & \text{Neem samen} \\ &=b^2-\frac{139}{56}b+\frac{78}{56} & \text{Maak de som} \\ &=b^2-\frac{139}{56}b+\frac{39}{28} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-11}{5})(b+\frac{-5}{17})& =(\color{red}{q}+\color{orange}{\frac{11}{5}}).(\color{green}{b}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{11}{5})} . \color{green}{(b)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{17}q+\frac{11}{5}b-\frac{11}{5}.\frac{5}{17}& \text{Uitwerken } \\ & =bq-\frac{5}{17}q+\frac{11}{5}b-\frac{55}{85} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{5}{17}q+\frac{11}{5}b-\frac{11}{17} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-6}{14})(b-\frac{8}{14})& =(\color{red}{p}+\color{orange}{\frac{3}{7}}).(\color{green}{b}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{3}{7})} . \color{green}{(b)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{7}p+\frac{3}{7}b-\frac{3}{7}.\frac{4}{7}& \text{Uitwerken } \\ & =bp-\frac{4}{7}p+\frac{3}{7}b-\frac{12}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{3}{12})(\frac{6}{9}+a)& =(\color{red}{x}+\color{orange}{\frac{-1}{4}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}x-\frac{1}{4}a-\frac{1}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}x-\frac{1}{4}a-\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{3}x-\frac{1}{4}a-\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-6}{3}-q)(q+\frac{-19}{10})& =(\color{red}{-q}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{19}{10}q-2q+2.\frac{19}{10}& \text{Uitwerken } \\ & =-q^2+(\frac{19}{10}+(-2))q+(\frac{-38}{10}) & \text{Neem samen} \\ &=-q^2-\frac{1}{10}q+(\frac{-38}{10}) & \text{Maak de som} \\ &=-q^2-\frac{1}{10}q+(\frac{-19}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-8}{14})(a+(-11))& =(\color{red}{x}+\color{orange}{\frac{-4}{7}}).(\color{green}{a}+\color{blue}{(-11)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-11)} + \color{orange}{(\frac{-4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = ax-11x-\frac{4}{7}a+\frac{4}{7}.11& \text{Uitwerken } \\ & =ax-11x-\frac{4}{7}a+\frac{44}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{4}{3}+p)(b+\frac{-5}{6})& =(\color{red}{p}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{6}p+\frac{4}{3}b-\frac{4}{3}.\frac{5}{6}& \text{Uitwerken } \\ & =bp-\frac{5}{6}p+\frac{4}{3}b-\frac{20}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{5}{6}p+\frac{4}{3}b-\frac{10}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{8}-q)(\frac{10}{19}-x)& =(\color{red}{-q}+\color{orange}{\frac{5}{4}}).(\color{green}{-x}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{10}{19}q-\frac{5}{4}x+\frac{5}{4}.\frac{10}{19}& \text{Uitwerken } \\ & =qx-\frac{10}{19}q-\frac{5}{4}x+\frac{50}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{10}{19}q-\frac{5}{4}x+\frac{25}{38} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-16}{12})(\frac{14}{13}-a)& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{-a}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{14}{13}b+\frac{4}{3}a-\frac{4}{3}.\frac{14}{13}& \text{Uitwerken } \\ & =-ab+\frac{14}{13}b+\frac{4}{3}a-\frac{56}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-12 14:22:53
Een site van Busleyden Atheneum Mechelen