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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{13}-q)(x-\frac{-17}{6})& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{17}{6}q-1x-1.\frac{17}{6}& \text{Uitwerken } \\ & =-qx-\frac{17}{6}q-1x-\frac{17}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-10}{9})(\frac{-19}{17}-p)& =(\color{red}{p}+\color{orange}{\frac{-10}{9}}).(\color{green}{-p}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{19}{17}p+\frac{10}{9}p+\frac{10}{9}.\frac{19}{17}& \text{Uitwerken } \\ & =-p^2+((\frac{-19}{17})+\frac{10}{9})p+(\frac{-190}{153}) & \text{Neem samen} \\ &=-p^2-\frac{1}{153}p+(\frac{-190}{153}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{16}-a)(a-\frac{14}{16})& =(\color{red}{-a}+\color{orange}{\frac{-7}{8}}).(\color{green}{a}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{7}{8}a-\frac{7}{8}a+\frac{7}{8}.\frac{7}{8}& \text{Uitwerken } \\ & =-a^2+(\frac{7}{8}+(\frac{-7}{8}))a+(\frac{-49}{64}) & \text{Neem samen} \\ &=-a^2+\frac{0}{8}a+(\frac{-49}{64}) & \text{Maak de som} \\ &=-a^2+0a+(\frac{-49}{64}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(x-7)(\frac{-6}{13}+x)& =(\color{red}{x}+\color{orange}{(-7)}).(\color{green}{x}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(-7)} . \color{green}{(x)} + \color{orange}{(-7)} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{6}{13}x-7x+7.\frac{6}{13}& \text{Uitwerken } \\ & =x^2+((\frac{-6}{13})+(-7))x+\frac{42}{13} & \text{Neem samen} \\ &=x^2-\frac{97}{13}x+\frac{42}{13} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(p-\frac{9}{20})(b+\frac{14}{19})& =(\color{red}{p}+\color{orange}{\frac{-9}{20}}).(\color{green}{b}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{14}{19}p-\frac{9}{20}b-\frac{9}{20}.\frac{14}{19}& \text{Uitwerken } \\ & =bp+\frac{14}{19}p-\frac{9}{20}b-\frac{126}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{14}{19}p-\frac{9}{20}b-\frac{63}{190} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{3}{12})(x+\frac{7}{14})& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{2}q-\frac{1}{4}x-\frac{1}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =qx+\frac{1}{2}q-\frac{1}{4}x-\frac{1}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{5}{9})(\frac{18}{4}+q)& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{q}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{2}b-\frac{5}{9}q-\frac{5}{9}.\frac{9}{2}& \text{Uitwerken } \\ & =bq+\frac{9}{2}b-\frac{5}{9}q-\frac{45}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{9}{2}b-\frac{5}{9}q-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-9}{10}+x)(q+\frac{9}{5})& =(\color{red}{x}+\color{orange}{\frac{-9}{10}}).(\color{green}{q}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{5}x-\frac{9}{10}q-\frac{9}{10}.\frac{9}{5}& \text{Uitwerken } \\ & =qx+\frac{9}{5}x-\frac{9}{10}q-\frac{81}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}((-13)-q)(q-\frac{-19}{6})& =(\color{red}{-q}+\color{orange}{(-13)}).(\color{green}{q}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(-13)} . \color{green}{(q)} + \color{orange}{(-13)} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{19}{6}q-13q-13.\frac{19}{6}& \text{Uitwerken } \\ & =-q^2+((\frac{-19}{6})+(-13))q-\frac{247}{6} & \text{Neem samen} \\ &=-q^2-\frac{97}{6}q-\frac{247}{6} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(b-\frac{8}{20})(a+17)& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{17})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(17)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = ab+17b-\frac{2}{5}a-\frac{2}{5}.17& \text{Uitwerken } \\ & =ab+17b-\frac{2}{5}a-\frac{34}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-7}{15})(\frac{-4}{2}-a)& =(\color{red}{q}+\color{orange}{\frac{-7}{15}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -aq-2q+\frac{7}{15}a+\frac{7}{15}.2& \text{Uitwerken } \\ & =-aq-2q+\frac{7}{15}a+\frac{14}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-13}{19})(\frac{-4}{20}-b)& =(\color{red}{q}+\color{orange}{\frac{-13}{19}}).(\color{green}{-b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{5}q+\frac{13}{19}b+\frac{13}{19}.\frac{1}{5}& \text{Uitwerken } \\ & =-bq-\frac{1}{5}q+\frac{13}{19}b+\frac{13}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-16 03:54:25
Een site van Busleyden Atheneum Mechelen