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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-10}{4}-p)(\frac{18}{8}-p)& =(\color{red}{-p}+\color{orange}{\frac{-5}{2}}).(\color{green}{-p}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{9}{4}p+\frac{5}{2}p-\frac{5}{2}.\frac{9}{4}& \text{Uitwerken } \\ & =p^2+((\frac{-9}{4})+\frac{5}{2})p-(\frac{-45}{8}) & \text{Neem samen} \\ &=p^2+\frac{1}{4}p-(\frac{-45}{8}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(a-\frac{6}{13})(\frac{-12}{4}-a)& =(\color{red}{a}+\color{orange}{\frac{-6}{13}}).(\color{green}{-a}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{-6}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -aa-3a+\frac{6}{13}a+\frac{6}{13}.3& \text{Uitwerken } \\ & =-a^2+((-3)+\frac{6}{13})a+(\frac{-18}{13}) & \text{Neem samen} \\ &=-a^2-\frac{33}{13}a+(\frac{-18}{13}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{17}{6}+x)(\frac{-19}{4}+b)& =(\color{red}{x}+\color{orange}{\frac{17}{6}}).(\color{green}{b}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{17}{6})} . \color{green}{(b)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{4}x+\frac{17}{6}b-\frac{17}{6}.\frac{19}{4}& \text{Uitwerken } \\ & =bx-\frac{19}{4}x+\frac{17}{6}b-\frac{323}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-8}{11})(q-\frac{-5}{13})& =(\color{red}{x}+\color{orange}{\frac{-8}{11}}).(\color{green}{q}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-8}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{13}x-\frac{8}{11}q-\frac{8}{11}.\frac{5}{13}& \text{Uitwerken } \\ & =qx+\frac{5}{13}x-\frac{8}{11}q-\frac{40}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-2}{16})(q-\frac{-19}{5})& =(\color{red}{b}+\color{orange}{\frac{1}{8}}).(\color{green}{q}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{1}{8})} . \color{green}{(q)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{5}b+\frac{1}{8}q+\frac{1}{8}.\frac{19}{5}& \text{Uitwerken } \\ & =bq+\frac{19}{5}b+\frac{1}{8}q+\frac{19}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{7}{10})(\frac{-17}{6}-a)& =(\color{red}{p}+\color{orange}{\frac{7}{10}}).(\color{green}{-a}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{7}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{6}p-\frac{7}{10}a-\frac{7}{10}.\frac{17}{6}& \text{Uitwerken } \\ & =-ap-\frac{17}{6}p-\frac{7}{10}a-\frac{119}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{14}{3})(\frac{18}{6}+a)& =(\color{red}{q}+\color{orange}{\frac{-14}{3}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{-14}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = aq+3q-\frac{14}{3}a-\frac{14}{3}.3& \text{Uitwerken } \\ & =aq+3q-\frac{14}{3}a-\frac{42}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+3q-\frac{14}{3}a-14 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-20}{7})(b+\frac{10}{10})& =(\color{red}{p}+\color{orange}{\frac{-20}{7}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-20}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p-\frac{20}{7}b-\frac{20}{7}.1& \text{Uitwerken } \\ & =bp+1p-\frac{20}{7}b-\frac{20}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{8}{4}-q)(q+\frac{-4}{16})& =(\color{red}{-q}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{1}{4}q+2q-2.\frac{1}{4}& \text{Uitwerken } \\ & =-q^2+(\frac{1}{4}+2)q-\frac{2}{4} & \text{Neem samen} \\ &=-q^2+\frac{9}{4}q-\frac{2}{4} & \text{Maak de som} \\ &=-q^2+\frac{9}{4}q-\frac{1}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{17}{17}+a)(x+\frac{-6}{7})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{6}{7}a+1x-1.\frac{6}{7}& \text{Uitwerken } \\ & =ax-\frac{6}{7}a+1x-\frac{6}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-4}{8}+a)(\frac{-15}{19}-x)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{-x}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{15}{19}a+\frac{1}{2}x+\frac{1}{2}.\frac{15}{19}& \text{Uitwerken } \\ & =-ax-\frac{15}{19}a+\frac{1}{2}x+\frac{15}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-18}{11})(\frac{-14}{15}+p)& =(\color{red}{b}+\color{orange}{\frac{18}{11}}).(\color{green}{p}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{18}{11})} . \color{green}{(p)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{14}{15}b+\frac{18}{11}p-\frac{18}{11}.\frac{14}{15}& \text{Uitwerken } \\ & =bp-\frac{14}{15}b+\frac{18}{11}p-\frac{252}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{14}{15}b+\frac{18}{11}p-\frac{84}{55} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-16 13:39:19
Een site van Busleyden Atheneum Mechelen