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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{5}{3})(q+9)& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{q}+\color{blue}{9})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(9)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = pq+9p-\frac{5}{3}q-\frac{5}{3}.9& \text{Uitwerken } \\ & =pq+9p-\frac{5}{3}q-\frac{45}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+9p-\frac{5}{3}q-15 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-4}{17}+p)(a-\frac{4}{18})& =(\color{red}{p}+\color{orange}{\frac{-4}{17}}).(\color{green}{a}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-4}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{9}p-\frac{4}{17}a+\frac{4}{17}.\frac{2}{9}& \text{Uitwerken } \\ & =ap-\frac{2}{9}p-\frac{4}{17}a+\frac{8}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-(-5))(\frac{-10}{19}-x)& =(\color{red}{q}+\color{orange}{5}).(\color{green}{-x}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(5)} . \color{green}{(-x)} + \color{orange}{(5)} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{10}{19}q-5x-5.\frac{10}{19}& \text{Uitwerken } \\ & =-qx-\frac{10}{19}q-5x-\frac{50}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-1}{18}-q)(\frac{19}{20}+x)& =(\color{red}{-q}+\color{orange}{\frac{-1}{18}}).(\color{green}{x}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{-1}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{20}q-\frac{1}{18}x-\frac{1}{18}.\frac{19}{20}& \text{Uitwerken } \\ & =-qx-\frac{19}{20}q-\frac{1}{18}x-\frac{19}{360} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{-15}{4})(p+\frac{-6}{8})& =(\color{red}{x}+\color{orange}{\frac{15}{4}}).(\color{green}{p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{15}{4})} . \color{green}{(p)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{4}x+\frac{15}{4}p-\frac{15}{4}.\frac{3}{4}& \text{Uitwerken } \\ & =px-\frac{3}{4}x+\frac{15}{4}p-\frac{45}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{1}{15}+p)(\frac{-14}{4}+q)& =(\color{red}{p}+\color{orange}{\frac{1}{15}}).(\color{green}{q}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{1}{15})} . \color{green}{(q)} + \color{orange}{(\frac{1}{15})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{2}p+\frac{1}{15}q-\frac{1}{15}.\frac{7}{2}& \text{Uitwerken } \\ & =pq-\frac{7}{2}p+\frac{1}{15}q-\frac{7}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{5}{19})(q+\frac{7}{5})& =(\color{red}{a}+\color{orange}{\frac{5}{19}}).(\color{green}{q}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{5}{19})} . \color{green}{(q)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{5}a+\frac{5}{19}q+\frac{5}{19}.\frac{7}{5}& \text{Uitwerken } \\ & =aq+\frac{7}{5}a+\frac{5}{19}q+\frac{35}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{7}{5}a+\frac{5}{19}q+\frac{7}{19} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{16}{19}-x)(x-\frac{-6}{4})& =(\color{red}{-x}+\color{orange}{\frac{16}{19}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{16}{19})} . \color{green}{(x)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{3}{2}x+\frac{16}{19}x+\frac{16}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =-x^2+((\frac{-3}{2})+\frac{16}{19})x+(\frac{-48}{38}) & \text{Neem samen} \\ &=-x^2-\frac{25}{38}x+(\frac{-48}{38}) & \text{Maak de som} \\ &=-x^2-\frac{25}{38}x+(\frac{-24}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-18}{14})(\frac{-15}{9}+p)& =(\color{red}{p}+\color{orange}{\frac{-9}{7}}).(\color{green}{p}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{3}p-\frac{9}{7}p+\frac{9}{7}.\frac{5}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{3})+(\frac{-9}{7}))p+\frac{45}{21} & \text{Neem samen} \\ &=p^2-\frac{62}{21}p+\frac{45}{21} & \text{Maak de som} \\ &=p^2-\frac{62}{21}p+\frac{15}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{10}{7}+x)(b-\frac{-3}{2})& =(\color{red}{x}+\color{orange}{\frac{10}{7}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{10}{7})} . \color{green}{(b)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{2}x+\frac{10}{7}b+\frac{10}{7}.\frac{3}{2}& \text{Uitwerken } \\ & =bx+\frac{3}{2}x+\frac{10}{7}b+\frac{30}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{2}x+\frac{10}{7}b+\frac{15}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a+\frac{16}{18})(a+\frac{-18}{8})& =(\color{red}{a}+\color{orange}{\frac{8}{9}}).(\color{green}{a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{9}{4}a+\frac{8}{9}a-\frac{8}{9}.\frac{9}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-9}{4})+\frac{8}{9})a-(\frac{-72}{36}) & \text{Neem samen} \\ &=a^2-\frac{49}{36}a-(\frac{-72}{36}) & \text{Maak de som} \\ &=a^2-\frac{49}{36}a+2 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{15}-b)(\frac{-12}{18}-p)& =(\color{red}{-b}+\color{orange}{\frac{3}{5}}).(\color{green}{-p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{3}b-\frac{3}{5}p-\frac{3}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =bp+\frac{2}{3}b-\frac{3}{5}p-\frac{6}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{3}b-\frac{3}{5}p-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-02 16:52:38
Een site van Busleyden Atheneum Mechelen