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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{16}{2})(\frac{-6}{2}+a)& =(\color{red}{a}+\color{orange}{(-8)}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(-8)} . \color{green}{(a)} + \color{orange}{(-8)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = aa-3a-8a+8.3& \text{Uitwerken } \\ & =a^2+((-3)+(-8))a+24 & \text{Neem samen} \\ &=a^2-11a+24 & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(x+\frac{8}{12})(q-\frac{-15}{18})& =(\color{red}{x}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{6}x+\frac{2}{3}q+\frac{2}{3}.\frac{5}{6}& \text{Uitwerken } \\ & =qx+\frac{5}{6}x+\frac{2}{3}q+\frac{10}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{5}{6}x+\frac{2}{3}q+\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p-\frac{6}{20})((-16)+a)& =(\color{red}{p}+\color{orange}{\frac{-3}{10}}).(\color{green}{a}+\color{blue}{(-16)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-16)} + \color{orange}{(\frac{-3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = ap-16p-\frac{3}{10}a+\frac{3}{10}.16& \text{Uitwerken } \\ & =ap-16p-\frac{3}{10}a+\frac{48}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-16p-\frac{3}{10}a+\frac{24}{5} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x-6)(\frac{-6}{11}-a)& =(\color{red}{x}+\color{orange}{(-6)}).(\color{green}{-a}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(-6)} . \color{green}{(-a)} + \color{orange}{(-6)} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{6}{11}x+6a+6.\frac{6}{11}& \text{Uitwerken } \\ & =-ax-\frac{6}{11}x+6a+\frac{36}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-2}{8}-q)(\frac{-2}{3}-x)& =(\color{red}{-q}+\color{orange}{\frac{-1}{4}}).(\color{green}{-x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{3}q+\frac{1}{4}x+\frac{1}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =qx+\frac{2}{3}q+\frac{1}{4}x+\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{2}{3}q+\frac{1}{4}x+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-6}{12})(\frac{-7}{4}+q)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{4}a-\frac{1}{2}q+\frac{1}{2}.\frac{7}{4}& \text{Uitwerken } \\ & =aq-\frac{7}{4}a-\frac{1}{2}q+\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-10}{2})(x-\frac{-5}{19})& =(\color{red}{p}+\color{orange}{5}).(\color{green}{x}+\color{blue}{\frac{5}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{19})} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(\frac{5}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{19}p+5x+5.\frac{5}{19}& \text{Uitwerken } \\ & =px+\frac{5}{19}p+5x+\frac{25}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{20}+a)(a-\frac{-8}{12})& =(\color{red}{a}+\color{orange}{\frac{-3}{20}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{2}{3}a-\frac{3}{20}a-\frac{3}{20}.\frac{2}{3}& \text{Uitwerken } \\ & =a^2+(\frac{2}{3}+(\frac{-3}{20}))a-(\frac{-6}{60}) & \text{Neem samen} \\ &=a^2+\frac{31}{60}a-(\frac{-6}{60}) & \text{Maak de som} \\ &=a^2+\frac{31}{60}a+\frac{1}{10} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{-18}{3}-x)(\frac{14}{2}+q)& =(\color{red}{-x}+\color{orange}{(-6)}).(\color{green}{q}+\color{blue}{7})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(7)} + \color{orange}{(-6)} . \color{green}{(q)} + \color{orange}{(-6)} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = -qx-7x-6q-6.7& \text{Uitwerken } \\ & =-qx-7x-6q-42 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-13}{17}+b)(q+\frac{-16}{17})& =(\color{red}{b}+\color{orange}{\frac{-13}{17}}).(\color{green}{q}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{16}{17}b-\frac{13}{17}q+\frac{13}{17}.\frac{16}{17}& \text{Uitwerken } \\ & =bq-\frac{16}{17}b-\frac{13}{17}q+\frac{208}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-1}{18})(\frac{-15}{13}-x)& =(\color{red}{b}+\color{orange}{\frac{1}{18}}).(\color{green}{-x}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{1}{18})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{15}{13}b-\frac{1}{18}x-\frac{1}{18}.\frac{15}{13}& \text{Uitwerken } \\ & =-bx-\frac{15}{13}b-\frac{1}{18}x-\frac{15}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{15}{13}b-\frac{1}{18}x-\frac{5}{78} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p+\frac{17}{19})(\frac{-11}{15}-p)& =(\color{red}{p}+\color{orange}{\frac{17}{19}}).(\color{green}{-p}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{17}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{11}{15}p-\frac{17}{19}p-\frac{17}{19}.\frac{11}{15}& \text{Uitwerken } \\ & =-p^2+((\frac{-11}{15})+(\frac{-17}{19}))p-\frac{187}{285} & \text{Neem samen} \\ &=-p^2-\frac{464}{285}p-\frac{187}{285} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-18 09:28:11
Een site van Busleyden Atheneum Mechelen