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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{12}{18})(q-\frac{-17}{3})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{17}{3}q+\frac{2}{3}q+\frac{2}{3}.\frac{17}{3}& \text{Uitwerken } \\ & =q^2+(\frac{17}{3}+\frac{2}{3})q+\frac{34}{9} & \text{Neem samen} \\ &=q^2+\frac{19}{3}q+\frac{34}{9} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{12}{3}+b)(p-\frac{-13}{12})& =(\color{red}{b}+\color{orange}{4}).(\color{green}{p}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{12}b+4p+4.\frac{13}{12}& \text{Uitwerken } \\ & =bp+\frac{13}{12}b+4p+\frac{52}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{13}{12}b+4p+\frac{13}{3} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-4}{14})(\frac{2}{5}-p)& =(\color{red}{q}+\color{orange}{\frac{2}{7}}).(\color{green}{-p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{2}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{2}{5}q-\frac{2}{7}p+\frac{2}{7}.\frac{2}{5}& \text{Uitwerken } \\ & =-pq+\frac{2}{5}q-\frac{2}{7}p+\frac{4}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-1}{17})(a+\frac{15}{10})& =(\color{red}{x}+\color{orange}{\frac{-1}{17}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{2}x-\frac{1}{17}a-\frac{1}{17}.\frac{3}{2}& \text{Uitwerken } \\ & =ax+\frac{3}{2}x-\frac{1}{17}a-\frac{3}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-10}{12})(b-\frac{-13}{20})& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{b}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{20}q-\frac{5}{6}b-\frac{5}{6}.\frac{13}{20}& \text{Uitwerken } \\ & =bq+\frac{13}{20}q-\frac{5}{6}b-\frac{65}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{13}{20}q-\frac{5}{6}b-\frac{13}{24} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-4}{13})(\frac{-8}{19}-a)& =(\color{red}{q}+\color{orange}{\frac{4}{13}}).(\color{green}{-a}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{4}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{8}{19}q-\frac{4}{13}a-\frac{4}{13}.\frac{8}{19}& \text{Uitwerken } \\ & =-aq-\frac{8}{19}q-\frac{4}{13}a-\frac{32}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-18}{19}+b)(\frac{-17}{2}-p)& =(\color{red}{b}+\color{orange}{\frac{-18}{19}}).(\color{green}{-p}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{17}{2}b+\frac{18}{19}p+\frac{18}{19}.\frac{17}{2}& \text{Uitwerken } \\ & =-bp-\frac{17}{2}b+\frac{18}{19}p+\frac{306}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{17}{2}b+\frac{18}{19}p+\frac{153}{19} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x+\frac{2}{6})(\frac{-12}{13}+x)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{12}{13}x+\frac{1}{3}x-\frac{1}{3}.\frac{12}{13}& \text{Uitwerken } \\ & =x^2+((\frac{-12}{13})+\frac{1}{3})x-(\frac{-12}{39}) & \text{Neem samen} \\ &=x^2-\frac{23}{39}x-(\frac{-12}{39}) & \text{Maak de som} \\ &=x^2-\frac{23}{39}x+\frac{4}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{-17}{8}-q)(q+\frac{1}{16})& =(\color{red}{-q}+\color{orange}{\frac{-17}{8}}).(\color{green}{q}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{-17}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{16}q-\frac{17}{8}q-\frac{17}{8}.\frac{1}{16}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{16})+(\frac{-17}{8}))q-\frac{17}{128} & \text{Neem samen} \\ &=-q^2-\frac{35}{16}q-\frac{17}{128} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-7}{15}+a)(\frac{-18}{12}-a)& =(\color{red}{a}+\color{orange}{\frac{-7}{15}}).(\color{green}{-a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{3}{2}a+\frac{7}{15}a+\frac{7}{15}.\frac{3}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-3}{2})+\frac{7}{15})a+(\frac{-21}{30}) & \text{Neem samen} \\ &=-a^2-\frac{31}{30}a+(\frac{-21}{30}) & \text{Maak de som} \\ &=-a^2-\frac{31}{30}a+(\frac{-7}{10}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-18}{13}-x)(\frac{-11}{3}-a)& =(\color{red}{-x}+\color{orange}{\frac{-18}{13}}).(\color{green}{-a}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{-18}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{3}x+\frac{18}{13}a+\frac{18}{13}.\frac{11}{3}& \text{Uitwerken } \\ & =ax+\frac{11}{3}x+\frac{18}{13}a+\frac{198}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{11}{3}x+\frac{18}{13}a+\frac{66}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}((-16)-x)(b-\frac{-19}{6})& =(\color{red}{-x}+\color{orange}{(-16)}).(\color{green}{b}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(-16)} . \color{green}{(b)} + \color{orange}{(-16)} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{19}{6}x-16b-16.\frac{19}{6}& \text{Uitwerken } \\ & =-bx-\frac{19}{6}x-16b-\frac{304}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{19}{6}x-16b-\frac{152}{3} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-28 21:42:37
Een site van Busleyden Atheneum Mechelen