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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{17}-p)(\frac{6}{11}+p)& =(\color{red}{-p}+\color{orange}{\frac{11}{17}}).(\color{green}{p}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{11}{17})} . \color{green}{(p)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{6}{11}p+\frac{11}{17}p+\frac{11}{17}.\frac{6}{11}& \text{Uitwerken } \\ & =-p^2+((\frac{-6}{11})+\frac{11}{17})p+(\frac{-66}{187}) & \text{Neem samen} \\ &=-p^2+\frac{19}{187}p+(\frac{-66}{187}) & \text{Maak de som} \\ &=-p^2+\frac{19}{187}p+(\frac{-6}{17}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-10}{15}+x)(\frac{5}{7}-p)& =(\color{red}{x}+\color{orange}{\frac{-2}{3}}).(\color{green}{-p}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{5}{7}x+\frac{2}{3}p-\frac{2}{3}.\frac{5}{7}& \text{Uitwerken } \\ & =-px+\frac{5}{7}x+\frac{2}{3}p-\frac{10}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{6}{7})(\frac{-4}{19}+p)& =(\color{red}{b}+\color{orange}{\frac{6}{7}}).(\color{green}{p}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{6}{7})} . \color{green}{(p)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{19}b+\frac{6}{7}p-\frac{6}{7}.\frac{4}{19}& \text{Uitwerken } \\ & =bp-\frac{4}{19}b+\frac{6}{7}p-\frac{24}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}((-17)+q)(\frac{18}{12}-b)& =(\color{red}{q}+\color{orange}{(-17)}).(\color{green}{-b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(-17)} . \color{green}{(-b)} + \color{orange}{(-17)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{2}q+17b-17.\frac{3}{2}& \text{Uitwerken } \\ & =-bq+\frac{3}{2}q+17b-\frac{51}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{17}+q)(a+\frac{4}{8})& =(\color{red}{q}+\color{orange}{\frac{-9}{17}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{2}q-\frac{9}{17}a-\frac{9}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =aq+\frac{1}{2}q-\frac{9}{17}a-\frac{9}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{16}-p)(\frac{-15}{11}+p)& =(\color{red}{-p}+\color{orange}{\frac{-7}{16}}).(\color{green}{p}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{-7}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{15}{11}p-\frac{7}{16}p+\frac{7}{16}.\frac{15}{11}& \text{Uitwerken } \\ & =-p^2+(\frac{15}{11}+(\frac{-7}{16}))p+(\frac{-105}{176}) & \text{Neem samen} \\ &=-p^2+\frac{163}{176}p+(\frac{-105}{176}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{15}-x)(\frac{17}{9}+p)& =(\color{red}{-x}+\color{orange}{\frac{8}{15}}).(\color{green}{p}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{8}{15})} . \color{green}{(p)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{17}{9}x+\frac{8}{15}p+\frac{8}{15}.\frac{17}{9}& \text{Uitwerken } \\ & =-px-\frac{17}{9}x+\frac{8}{15}p+\frac{136}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{2}{19})(q-\frac{11}{15})& =(\color{red}{q}+\color{orange}{\frac{2}{19}}).(\color{green}{q}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{2}{19})} . \color{green}{(q)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{15}q+\frac{2}{19}q-\frac{2}{19}.\frac{11}{15}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{15})+\frac{2}{19})q-(\frac{-22}{285}) & \text{Neem samen} \\ &=q^2-\frac{179}{285}q-(\frac{-22}{285}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-18}{18}-b)(\frac{-18}{10}-x)& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{5}b+1x+1.\frac{9}{5}& \text{Uitwerken } \\ & =bx+\frac{9}{5}b+1x+\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-10}{13})(\frac{18}{8}+x)& =(\color{red}{q}+\color{orange}{\frac{10}{13}}).(\color{green}{x}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{10}{13})} . \color{green}{(x)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{4}q+\frac{10}{13}x+\frac{10}{13}.\frac{9}{4}& \text{Uitwerken } \\ & =qx+\frac{9}{4}q+\frac{10}{13}x+\frac{90}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{9}{4}q+\frac{10}{13}x+\frac{45}{26} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{14}{14})(\frac{17}{9}+b)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{9}x-1b-1.\frac{17}{9}& \text{Uitwerken } \\ & =bx+\frac{17}{9}x-1b-\frac{17}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-15}{14})(b-\frac{11}{9})& =(\color{red}{x}+\color{orange}{\frac{-15}{14}}).(\color{green}{b}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{9}x-\frac{15}{14}b+\frac{15}{14}.\frac{11}{9}& \text{Uitwerken } \\ & =bx-\frac{11}{9}x-\frac{15}{14}b+\frac{165}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{11}{9}x-\frac{15}{14}b+\frac{55}{42} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-27 13:23:21
Een site van Busleyden Atheneum Mechelen