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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{13}-a)(\frac{-12}{6}+x)& =(\color{red}{-a}+\color{orange}{\frac{15}{13}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(-2)} + \color{orange}{(\frac{15}{13})} . \color{green}{(x)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ax+2a+\frac{15}{13}x-\frac{15}{13}.2& \text{Uitwerken } \\ & =-ax+2a+\frac{15}{13}x-\frac{30}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-18}{7})(p-\frac{4}{15})& =(\color{red}{p}+\color{orange}{\frac{18}{7}}).(\color{green}{p}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{18}{7})} . \color{green}{(p)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{4}{15}p+\frac{18}{7}p-\frac{18}{7}.\frac{4}{15}& \text{Uitwerken } \\ & =p^2+((\frac{-4}{15})+\frac{18}{7})p-(\frac{-72}{105}) & \text{Neem samen} \\ &=p^2+\frac{242}{105}p-(\frac{-72}{105}) & \text{Maak de som} \\ &=p^2+\frac{242}{105}p+\frac{24}{35} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-9}{12})(\frac{14}{10}+p)& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{p}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{7}{5}p-\frac{3}{4}p-\frac{3}{4}.\frac{7}{5}& \text{Uitwerken } \\ & =p^2+(\frac{7}{5}+(\frac{-3}{4}))p-(\frac{-21}{20}) & \text{Neem samen} \\ &=p^2+\frac{13}{20}p-(\frac{-21}{20}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-13}{8})(13-b)& =(\color{red}{x}+\color{orange}{\frac{13}{8}}).(\color{green}{-b}+\color{blue}{13})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(13)} + \color{orange}{(\frac{13}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = -bx+13x-\frac{13}{8}b+\frac{13}{8}.13& \text{Uitwerken } \\ & =-bx+13x-\frac{13}{8}b+\frac{169}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-3}{10})(\frac{2}{8}+x)& =(\color{red}{x}+\color{orange}{\frac{-3}{10}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{4}x-\frac{3}{10}x-\frac{3}{10}.\frac{1}{4}& \text{Uitwerken } \\ & =x^2+(\frac{1}{4}+(\frac{-3}{10}))x-(\frac{-3}{40}) & \text{Neem samen} \\ &=x^2-\frac{1}{20}x-(\frac{-3}{40}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-4}{18})(\frac{-11}{2}+q)& =(\color{red}{p}+\color{orange}{\frac{2}{9}}).(\color{green}{q}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{2}{9})} . \color{green}{(q)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{2}p+\frac{2}{9}q-\frac{2}{9}.\frac{11}{2}& \text{Uitwerken } \\ & =pq-\frac{11}{2}p+\frac{2}{9}q-\frac{22}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{11}{2}p+\frac{2}{9}q-\frac{11}{9} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{5}{5}-p)(b+\frac{-9}{16})& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{16}p+1b-1.\frac{9}{16}& \text{Uitwerken } \\ & =-bp+\frac{9}{16}p+1b-\frac{9}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{5}{7})(a-\frac{2}{5})& =(\color{red}{x}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{5}x-\frac{5}{7}a+\frac{5}{7}.\frac{2}{5}& \text{Uitwerken } \\ & =ax-\frac{2}{5}x-\frac{5}{7}a+\frac{10}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{2}{5}x-\frac{5}{7}a+\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-5}{6})(p-\frac{20}{3})& =(\color{red}{q}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{20}{3}q+\frac{5}{6}p-\frac{5}{6}.\frac{20}{3}& \text{Uitwerken } \\ & =pq-\frac{20}{3}q+\frac{5}{6}p-\frac{100}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{20}{3}q+\frac{5}{6}p-\frac{50}{9} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{5}{2})(7+a)& =(\color{red}{a}+\color{orange}{\frac{5}{2}}).(\color{green}{a}+\color{blue}{7})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(7)} + \color{orange}{(\frac{5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = aa+7a+\frac{5}{2}a+\frac{5}{2}.7& \text{Uitwerken } \\ & =a^2+(7+\frac{5}{2})a+\frac{35}{2} & \text{Neem samen} \\ &=a^2+\frac{19}{2}a+\frac{35}{2} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-3}{2}+q)(\frac{-16}{12}-x)& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{-x}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{4}{3}q+\frac{3}{2}x+\frac{3}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =-qx-\frac{4}{3}q+\frac{3}{2}x+\frac{12}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{4}{3}q+\frac{3}{2}x+2 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-7}{6}+x)(\frac{-10}{3}+b)& =(\color{red}{x}+\color{orange}{\frac{-7}{6}}).(\color{green}{b}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{10}{3}x-\frac{7}{6}b+\frac{7}{6}.\frac{10}{3}& \text{Uitwerken } \\ & =bx-\frac{10}{3}x-\frac{7}{6}b+\frac{70}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{10}{3}x-\frac{7}{6}b+\frac{35}{9} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-11-14 21:51:23
Een site van Busleyden Atheneum Mechelen