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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-10}{17}-b)(q-(-3))& =(\color{red}{-b}+\color{orange}{\frac{-10}{17}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(3)} + \color{orange}{(\frac{-10}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -bq-3b-\frac{10}{17}q-\frac{10}{17}.3& \text{Uitwerken } \\ & =-bq-3b-\frac{10}{17}q-\frac{30}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{12}-q)((-6)+a)& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{(-6)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-6)} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -aq+6q-1a+1.6& \text{Uitwerken } \\ & =-aq+6q-1a+6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-13}{11})(\frac{-19}{8}+x)& =(\color{red}{a}+\color{orange}{\frac{-13}{11}}).(\color{green}{x}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{-13}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{8}a-\frac{13}{11}x+\frac{13}{11}.\frac{19}{8}& \text{Uitwerken } \\ & =ax-\frac{19}{8}a-\frac{13}{11}x+\frac{247}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-17}{15}+x)(\frac{-15}{16}-b)& =(\color{red}{x}+\color{orange}{\frac{-17}{15}}).(\color{green}{-b}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{15}{16}x+\frac{17}{15}b+\frac{17}{15}.\frac{15}{16}& \text{Uitwerken } \\ & =-bx-\frac{15}{16}x+\frac{17}{15}b+\frac{255}{240} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{15}{16}x+\frac{17}{15}b+\frac{17}{16} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-5}{11}-x)(b-\frac{-15}{8})& =(\color{red}{-x}+\color{orange}{\frac{-5}{11}}).(\color{green}{b}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{15}{8}x-\frac{5}{11}b-\frac{5}{11}.\frac{15}{8}& \text{Uitwerken } \\ & =-bx-\frac{15}{8}x-\frac{5}{11}b-\frac{75}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{4}+x)(p+\frac{-15}{11})& =(\color{red}{x}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{15}{11}x+5p-5.\frac{15}{11}& \text{Uitwerken } \\ & =px-\frac{15}{11}x+5p-\frac{75}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-(-17))(\frac{-3}{13}-x)& =(\color{red}{a}+\color{orange}{17}).(\color{green}{-x}+\color{blue}{\frac{-3}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{13})} + \color{orange}{(17)} . \color{green}{(-x)} + \color{orange}{(17)} . \color{blue}{(\frac{-3}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{13}a-17x-17.\frac{3}{13}& \text{Uitwerken } \\ & =-ax-\frac{3}{13}a-17x-\frac{51}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-5}{13})(\frac{2}{2}+a)& =(\color{red}{a}+\color{orange}{\frac{-5}{13}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-5}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aa+1a-\frac{5}{13}a-\frac{5}{13}.1& \text{Uitwerken } \\ & =a^2+(1+(\frac{-5}{13}))a-(\frac{-5}{13}) & \text{Neem samen} \\ &=a^2+\frac{8}{13}a-(\frac{-5}{13}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-19}{9})(b+\frac{20}{5})& =(\color{red}{a}+\color{orange}{\frac{19}{9}}).(\color{green}{b}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{19}{9})} . \color{green}{(b)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ab+4a+\frac{19}{9}b+\frac{19}{9}.4& \text{Uitwerken } \\ & =ab+4a+\frac{19}{9}b+\frac{76}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{20}{6})(\frac{-9}{9}+p)& =(\color{red}{b}+\color{orange}{\frac{-10}{3}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bp-1b-\frac{10}{3}p+\frac{10}{3}.1& \text{Uitwerken } \\ & =bp-1b-\frac{10}{3}p+\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-18}{20}-q)(q+\frac{8}{10})& =(\color{red}{-q}+\color{orange}{\frac{-9}{10}}).(\color{green}{q}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{4}{5}q-\frac{9}{10}q-\frac{9}{10}.\frac{4}{5}& \text{Uitwerken } \\ & =-q^2+((\frac{-4}{5})+(\frac{-9}{10}))q-\frac{36}{50} & \text{Neem samen} \\ &=-q^2-\frac{17}{10}q-\frac{36}{50} & \text{Maak de som} \\ &=-q^2-\frac{17}{10}q-\frac{18}{25} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{-20}{16}-p)(\frac{-20}{4}+a)& =(\color{red}{-p}+\color{orange}{\frac{-5}{4}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(-5)} + \color{orange}{(\frac{-5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -ap+5p-\frac{5}{4}a+\frac{5}{4}.5& \text{Uitwerken } \\ & =-ap+5p-\frac{5}{4}a+\frac{25}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-17 15:45:47
Een site van Busleyden Atheneum Mechelen