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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-12}{2})(\frac{-2}{4}-a)& =(\color{red}{p}+\color{orange}{6}).(\color{green}{-a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(6)} . \color{green}{(-a)} + \color{orange}{(6)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{2}p-6a-6.\frac{1}{2}& \text{Uitwerken } \\ & =-ap-\frac{1}{2}p-6a-\frac{6}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{1}{2}p-6a-3 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-15}{3}+x)(\frac{-12}{10}-a)& =(\color{red}{x}+\color{orange}{(-5)}).(\color{green}{-a}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(-5)} . \color{green}{(-a)} + \color{orange}{(-5)} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{6}{5}x+5a+5.\frac{6}{5}& \text{Uitwerken } \\ & =-ax-\frac{6}{5}x+5a+\frac{30}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{6}{5}x+5a+6 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{7}{10}-p)(a+\frac{-6}{18})& =(\color{red}{-p}+\color{orange}{\frac{7}{10}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{3}p+\frac{7}{10}a-\frac{7}{10}.\frac{1}{3}& \text{Uitwerken } \\ & =-ap+\frac{1}{3}p+\frac{7}{10}a-\frac{7}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{-13}{3})(b-\frac{18}{5})& =(\color{red}{b}+\color{orange}{\frac{13}{3}}).(\color{green}{b}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{13}{3})} . \color{green}{(b)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{18}{5}b+\frac{13}{3}b-\frac{13}{3}.\frac{18}{5}& \text{Uitwerken } \\ & =b^2+((\frac{-18}{5})+\frac{13}{3})b-(\frac{-234}{15}) & \text{Neem samen} \\ &=b^2+\frac{11}{15}b-(\frac{-234}{15}) & \text{Maak de som} \\ &=b^2+\frac{11}{15}b+\frac{78}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-18}{15})((-10)+q)& =(\color{red}{q}+\color{orange}{\frac{-6}{5}}).(\color{green}{q}+\color{blue}{(-10)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-10)} + \color{orange}{(\frac{-6}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = qq-10q-\frac{6}{5}q+\frac{6}{5}.10& \text{Uitwerken } \\ & =q^2+((-10)+(\frac{-6}{5}))q+\frac{60}{5} & \text{Neem samen} \\ &=q^2-\frac{56}{5}q+\frac{60}{5} & \text{Maak de som} \\ &=q^2-\frac{56}{5}q+12 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{13}{18}+a)(q-\frac{-19}{4})& =(\color{red}{a}+\color{orange}{\frac{13}{18}}).(\color{green}{q}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{13}{18})} . \color{green}{(q)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{4}a+\frac{13}{18}q+\frac{13}{18}.\frac{19}{4}& \text{Uitwerken } \\ & =aq+\frac{19}{4}a+\frac{13}{18}q+\frac{247}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{8}{14})(\frac{-12}{8}+x)& =(\color{red}{x}+\color{orange}{\frac{-4}{7}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{2}x-\frac{4}{7}x+\frac{4}{7}.\frac{3}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{2})+(\frac{-4}{7}))x+\frac{12}{14} & \text{Neem samen} \\ &=x^2-\frac{29}{14}x+\frac{12}{14} & \text{Maak de som} \\ &=x^2-\frac{29}{14}x+\frac{6}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-12}{13}+q)(\frac{-8}{14}+a)& =(\color{red}{q}+\color{orange}{\frac{-12}{13}}).(\color{green}{a}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{7}q-\frac{12}{13}a+\frac{12}{13}.\frac{4}{7}& \text{Uitwerken } \\ & =aq-\frac{4}{7}q-\frac{12}{13}a+\frac{48}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{14}-x)(a-\frac{-12}{20})& =(\color{red}{-x}+\color{orange}{\frac{2}{7}}).(\color{green}{a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{2}{7})} . \color{green}{(a)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{5}x+\frac{2}{7}a+\frac{2}{7}.\frac{3}{5}& \text{Uitwerken } \\ & =-ax-\frac{3}{5}x+\frac{2}{7}a+\frac{6}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{11}{9}+b)(\frac{16}{7}+x)& =(\color{red}{b}+\color{orange}{\frac{11}{9}}).(\color{green}{x}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{11}{9})} . \color{green}{(x)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{16}{7}b+\frac{11}{9}x+\frac{11}{9}.\frac{16}{7}& \text{Uitwerken } \\ & =bx+\frac{16}{7}b+\frac{11}{9}x+\frac{176}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{3}{5})(\frac{19}{3}-q)& =(\color{red}{q}+\color{orange}{\frac{-3}{5}}).(\color{green}{-q}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{19}{3}q+\frac{3}{5}q-\frac{3}{5}.\frac{19}{3}& \text{Uitwerken } \\ & =-q^2+(\frac{19}{3}+\frac{3}{5})q-\frac{57}{15} & \text{Neem samen} \\ &=-q^2+\frac{104}{15}q-\frac{57}{15} & \text{Maak de som} \\ &=-q^2+\frac{104}{15}q-\frac{19}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{-19}{10}-x)(b-\frac{18}{18})& =(\color{red}{-x}+\color{orange}{\frac{-19}{10}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-19}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1x-\frac{19}{10}b+\frac{19}{10}.1& \text{Uitwerken } \\ & =-bx+1x-\frac{19}{10}b+\frac{19}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-30 21:10:36
Een site van Busleyden Atheneum Mechelen