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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{2}+x)(q-\frac{2}{13})& =(\color{red}{x}+\color{orange}{\frac{15}{2}}).(\color{green}{q}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{15}{2})} . \color{green}{(q)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{13}x+\frac{15}{2}q-\frac{15}{2}.\frac{2}{13}& \text{Uitwerken } \\ & =qx-\frac{2}{13}x+\frac{15}{2}q-\frac{30}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{2}{13}x+\frac{15}{2}q-\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-16}{11})(\frac{12}{5}+b)& =(\color{red}{q}+\color{orange}{\frac{16}{11}}).(\color{green}{b}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{16}{11})} . \color{green}{(b)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{12}{5}q+\frac{16}{11}b+\frac{16}{11}.\frac{12}{5}& \text{Uitwerken } \\ & =bq+\frac{12}{5}q+\frac{16}{11}b+\frac{192}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{11}{16})(\frac{8}{4}+p)& =(\color{red}{a}+\color{orange}{\frac{11}{16}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{11}{16})} . \color{green}{(p)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2a+\frac{11}{16}p+\frac{11}{16}.2& \text{Uitwerken } \\ & =ap+2a+\frac{11}{16}p+\frac{22}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+2a+\frac{11}{16}p+\frac{11}{8} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{17}{14}-x)(\frac{-9}{15}-p)& =(\color{red}{-x}+\color{orange}{\frac{17}{14}}).(\color{green}{-p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{17}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{5}x-\frac{17}{14}p-\frac{17}{14}.\frac{3}{5}& \text{Uitwerken } \\ & =px+\frac{3}{5}x-\frac{17}{14}p-\frac{51}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-3}{3}+q)(x-\frac{8}{8})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1q-1x+1.1& \text{Uitwerken } \\ & =qx-1q-1x+1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{10}{14})(b+\frac{-19}{2})& =(\color{red}{x}+\color{orange}{\frac{5}{7}}).(\color{green}{b}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{5}{7})} . \color{green}{(b)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{2}x+\frac{5}{7}b-\frac{5}{7}.\frac{19}{2}& \text{Uitwerken } \\ & =bx-\frac{19}{2}x+\frac{5}{7}b-\frac{95}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{8}{7})(q+\frac{-16}{9})& =(\color{red}{q}+\color{orange}{\frac{8}{7}}).(\color{green}{q}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{16}{9}q+\frac{8}{7}q-\frac{8}{7}.\frac{16}{9}& \text{Uitwerken } \\ & =q^2+((\frac{-16}{9})+\frac{8}{7})q-(\frac{-128}{63}) & \text{Neem samen} \\ &=q^2-\frac{40}{63}q-(\frac{-128}{63}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{10}{16}-x)(b+\frac{6}{6})& =(\color{red}{-x}+\color{orange}{\frac{5}{8}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{8})} . \color{green}{(b)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx-1x+\frac{5}{8}b+\frac{5}{8}.1& \text{Uitwerken } \\ & =-bx-1x+\frac{5}{8}b+\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{-9}{13})(q+\frac{6}{10})& =(\color{red}{q}+\color{orange}{\frac{-9}{13}}).(\color{green}{q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{5}q-\frac{9}{13}q-\frac{9}{13}.\frac{3}{5}& \text{Uitwerken } \\ & =q^2+(\frac{3}{5}+(\frac{-9}{13}))q-(\frac{-27}{65}) & \text{Neem samen} \\ &=q^2-\frac{6}{65}q-(\frac{-27}{65}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-9}{16})(\frac{-10}{6}-q)& =(\color{red}{x}+\color{orange}{\frac{9}{16}}).(\color{green}{-q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{9}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{5}{3}x-\frac{9}{16}q-\frac{9}{16}.\frac{5}{3}& \text{Uitwerken } \\ & =-qx-\frac{5}{3}x-\frac{9}{16}q-\frac{45}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{5}{3}x-\frac{9}{16}q-\frac{15}{16} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{4}{20})(p+\frac{-1}{16})& =(\color{red}{q}+\color{orange}{\frac{1}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{16}q+\frac{1}{5}p-\frac{1}{5}.\frac{1}{16}& \text{Uitwerken } \\ & =pq-\frac{1}{16}q+\frac{1}{5}p-\frac{1}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-3}{10}+q)(\frac{-20}{7}+a)& =(\color{red}{q}+\color{orange}{\frac{-3}{10}}).(\color{green}{a}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{20}{7}q-\frac{3}{10}a+\frac{3}{10}.\frac{20}{7}& \text{Uitwerken } \\ & =aq-\frac{20}{7}q-\frac{3}{10}a+\frac{60}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{20}{7}q-\frac{3}{10}a+\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-01 17:39:52
Een site van Busleyden Atheneum Mechelen