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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-8}{13})(\frac{3}{5}-a)& =(\color{red}{q}+\color{orange}{\frac{-8}{13}}).(\color{green}{-a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-8}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-8}{13})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{5}q+\frac{8}{13}a-\frac{8}{13}.\frac{3}{5}& \text{Uitwerken } \\ & =-aq+\frac{3}{5}q+\frac{8}{13}a-\frac{24}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-14}{15}+x)(b+\frac{9}{3})& =(\color{red}{x}+\color{orange}{\frac{-14}{15}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{-14}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bx+3x-\frac{14}{15}b-\frac{14}{15}.3& \text{Uitwerken } \\ & =bx+3x-\frac{14}{15}b-\frac{42}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+3x-\frac{14}{15}b-\frac{14}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{9}{10})(\frac{18}{2}+a)& =(\color{red}{x}+\color{orange}{\frac{-9}{10}}).(\color{green}{a}+\color{blue}{9})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(9)} + \color{orange}{(\frac{-9}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = ax+9x-\frac{9}{10}a-\frac{9}{10}.9& \text{Uitwerken } \\ & =ax+9x-\frac{9}{10}a-\frac{81}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{1}{17}+q)(\frac{-2}{8}-b)& =(\color{red}{q}+\color{orange}{\frac{1}{17}}).(\color{green}{-b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{1}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{4}q-\frac{1}{17}b-\frac{1}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =-bq-\frac{1}{4}q-\frac{1}{17}b-\frac{1}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-13}{7})(x+\frac{-16}{8})& =(\color{red}{q}+\color{orange}{\frac{13}{7}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{13}{7})} . \color{green}{(x)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx-2q+\frac{13}{7}x-\frac{13}{7}.2& \text{Uitwerken } \\ & =qx-2q+\frac{13}{7}x-\frac{26}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-4}{5}-b)(\frac{10}{19}+q)& =(\color{red}{-b}+\color{orange}{\frac{-4}{5}}).(\color{green}{q}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{10}{19}b-\frac{4}{5}q-\frac{4}{5}.\frac{10}{19}& \text{Uitwerken } \\ & =-bq-\frac{10}{19}b-\frac{4}{5}q-\frac{40}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{10}{19}b-\frac{4}{5}q-\frac{8}{19} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{18}{17}-p)(\frac{17}{18}-q)& =(\color{red}{-p}+\color{orange}{\frac{18}{17}}).(\color{green}{-q}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{18}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{18}p-\frac{18}{17}q+\frac{18}{17}.\frac{17}{18}& \text{Uitwerken } \\ & =pq-\frac{17}{18}p-\frac{18}{17}q+\frac{306}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{17}{18}p-\frac{18}{17}q+1 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{6}{12})(q+\frac{-5}{19})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{19}b+\frac{1}{2}q-\frac{1}{2}.\frac{5}{19}& \text{Uitwerken } \\ & =bq-\frac{5}{19}b+\frac{1}{2}q-\frac{5}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-4}{18})(q-\frac{5}{7})& =(\color{red}{b}+\color{orange}{\frac{-2}{9}}).(\color{green}{q}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{7}b-\frac{2}{9}q+\frac{2}{9}.\frac{5}{7}& \text{Uitwerken } \\ & =bq-\frac{5}{7}b-\frac{2}{9}q+\frac{10}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-13}{18}+p)(p-\frac{-9}{14})& =(\color{red}{p}+\color{orange}{\frac{-13}{18}}).(\color{green}{p}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{14}p-\frac{13}{18}p-\frac{13}{18}.\frac{9}{14}& \text{Uitwerken } \\ & =p^2+(\frac{9}{14}+(\frac{-13}{18}))p-(\frac{-117}{252}) & \text{Neem samen} \\ &=p^2-\frac{10}{126}p-(\frac{-117}{252}) & \text{Maak de som} \\ &=p^2-\frac{5}{63}p+\frac{13}{28} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-13}{2})(\frac{17}{11}-x)& =(\color{red}{b}+\color{orange}{\frac{-13}{2}}).(\color{green}{-x}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{17}{11}b+\frac{13}{2}x-\frac{13}{2}.\frac{17}{11}& \text{Uitwerken } \\ & =-bx+\frac{17}{11}b+\frac{13}{2}x-\frac{221}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-12}{4}+p)(\frac{10}{8}-q)& =(\color{red}{p}+\color{orange}{(-3)}).(\color{green}{-q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(-3)} . \color{green}{(-q)} + \color{orange}{(-3)} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{4}p+3q-3.\frac{5}{4}& \text{Uitwerken } \\ & =-pq+\frac{5}{4}p+3q-\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-25 17:53:41
Een site van Busleyden Atheneum Mechelen