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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-5}{8}-q)(\frac{14}{16}+p)& =(\color{red}{-q}+\color{orange}{\frac{-5}{8}}).(\color{green}{p}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{7}{8}q-\frac{5}{8}p-\frac{5}{8}.\frac{7}{8}& \text{Uitwerken } \\ & =-pq-\frac{7}{8}q-\frac{5}{8}p-\frac{35}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-13}{18})(a-\frac{6}{12})& =(\color{red}{x}+\color{orange}{\frac{13}{18}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{13}{18})} . \color{green}{(a)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{2}x+\frac{13}{18}a-\frac{13}{18}.\frac{1}{2}& \text{Uitwerken } \\ & =ax-\frac{1}{2}x+\frac{13}{18}a-\frac{13}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-1}{13}+q)(\frac{-4}{19}-x)& =(\color{red}{q}+\color{orange}{\frac{-1}{13}}).(\color{green}{-x}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{4}{19}q+\frac{1}{13}x+\frac{1}{13}.\frac{4}{19}& \text{Uitwerken } \\ & =-qx-\frac{4}{19}q+\frac{1}{13}x+\frac{4}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-10}{20})(p+(-1))& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1x+\frac{1}{2}p-\frac{1}{2}.1& \text{Uitwerken } \\ & =px-1x+\frac{1}{2}p-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-20}{3}-b)(\frac{-19}{8}-a)& =(\color{red}{-b}+\color{orange}{\frac{-20}{3}}).(\color{green}{-a}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{8}b+\frac{20}{3}a+\frac{20}{3}.\frac{19}{8}& \text{Uitwerken } \\ & =ab+\frac{19}{8}b+\frac{20}{3}a+\frac{380}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{19}{8}b+\frac{20}{3}a+\frac{95}{6} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{2}{2}-p)(q+\frac{-11}{15})& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{15}p+1q-1.\frac{11}{15}& \text{Uitwerken } \\ & =-pq+\frac{11}{15}p+1q-\frac{11}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{3}{19})(\frac{10}{19}-b)& =(\color{red}{q}+\color{orange}{\frac{3}{19}}).(\color{green}{-b}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{3}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{19})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{10}{19}q-\frac{3}{19}b+\frac{3}{19}.\frac{10}{19}& \text{Uitwerken } \\ & =-bq+\frac{10}{19}q-\frac{3}{19}b+\frac{30}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{5}{5})(x-\frac{-16}{15})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{16}{15}a-1x-1.\frac{16}{15}& \text{Uitwerken } \\ & =ax+\frac{16}{15}a-1x-\frac{16}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-7}{17})(\frac{-3}{7}-p)& =(\color{red}{a}+\color{orange}{\frac{-7}{17}}).(\color{green}{-p}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{7}a+\frac{7}{17}p+\frac{7}{17}.\frac{3}{7}& \text{Uitwerken } \\ & =-ap-\frac{3}{7}a+\frac{7}{17}p+\frac{21}{119} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{3}{7}a+\frac{7}{17}p+\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-9}{17}+q)(\frac{19}{2}-q)& =(\color{red}{q}+\color{orange}{\frac{-9}{17}}).(\color{green}{-q}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{19}{2}q+\frac{9}{17}q-\frac{9}{17}.\frac{19}{2}& \text{Uitwerken } \\ & =-q^2+(\frac{19}{2}+\frac{9}{17})q-\frac{171}{34} & \text{Neem samen} \\ &=-q^2+\frac{341}{34}q-\frac{171}{34} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(x+(-19))(a+\frac{-17}{19})& =(\color{red}{x}+\color{orange}{(-19)}).(\color{green}{a}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(-19)} . \color{green}{(a)} + \color{orange}{(-19)} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{19}x-19a+19.\frac{17}{19}& \text{Uitwerken } \\ & =ax-\frac{17}{19}x-19a+\frac{323}{19} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{17}{19}x-19a+17 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{17}{8}-b)(x-\frac{-4}{5})& =(\color{red}{-b}+\color{orange}{\frac{17}{8}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{17}{8})} . \color{green}{(x)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{5}b+\frac{17}{8}x+\frac{17}{8}.\frac{4}{5}& \text{Uitwerken } \\ & =-bx-\frac{4}{5}b+\frac{17}{8}x+\frac{68}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{4}{5}b+\frac{17}{8}x+\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-28 19:55:37
Een site van Busleyden Atheneum Mechelen