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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-8}{5})(x-(-17))& =(\color{red}{x}+\color{orange}{\frac{8}{5}}).(\color{green}{x}+\color{blue}{17})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(17)} + \color{orange}{(\frac{8}{5})} . \color{green}{(x)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = xx+17x+\frac{8}{5}x+\frac{8}{5}.17& \text{Uitwerken } \\ & =x^2+(17+\frac{8}{5})x+\frac{136}{5} & \text{Neem samen} \\ &=x^2+\frac{93}{5}x+\frac{136}{5} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(a-\frac{14}{12})(p-\frac{5}{19})& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{p}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{19}a-\frac{7}{6}p+\frac{7}{6}.\frac{5}{19}& \text{Uitwerken } \\ & =ap-\frac{5}{19}a-\frac{7}{6}p+\frac{35}{114} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{19}{10})(\frac{-10}{20}+b)& =(\color{red}{x}+\color{orange}{\frac{19}{10}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{19}{10})} . \color{green}{(b)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}x+\frac{19}{10}b-\frac{19}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}x+\frac{19}{10}b-\frac{19}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{12}{12})(\frac{-1}{20}+q)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{20}x-1q+1.\frac{1}{20}& \text{Uitwerken } \\ & =qx-\frac{1}{20}x-1q+\frac{1}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{7}{3})(a-\frac{19}{16})& =(\color{red}{a}+\color{orange}{\frac{-7}{3}}).(\color{green}{a}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{19}{16}a-\frac{7}{3}a+\frac{7}{3}.\frac{19}{16}& \text{Uitwerken } \\ & =a^2+((\frac{-19}{16})+(\frac{-7}{3}))a+\frac{133}{48} & \text{Neem samen} \\ &=a^2-\frac{169}{48}a+\frac{133}{48} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-9}{16})(\frac{-18}{5}-b)& =(\color{red}{b}+\color{orange}{\frac{-9}{16}}).(\color{green}{-b}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{18}{5}b+\frac{9}{16}b+\frac{9}{16}.\frac{18}{5}& \text{Uitwerken } \\ & =-b^2+((\frac{-18}{5})+\frac{9}{16})b+(\frac{-162}{80}) & \text{Neem samen} \\ &=-b^2-\frac{243}{80}b+(\frac{-162}{80}) & \text{Maak de som} \\ &=-b^2-\frac{243}{80}b+(\frac{-81}{40}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{6}{8}-x)(\frac{20}{20}-x)& =(\color{red}{-x}+\color{orange}{\frac{3}{4}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = xx-1x-\frac{3}{4}x+\frac{3}{4}.1& \text{Uitwerken } \\ & =x^2+((-1)+(\frac{-3}{4}))x+\frac{3}{4} & \text{Neem samen} \\ &=x^2-\frac{7}{4}x+\frac{3}{4} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{15}{5}-q)(\frac{6}{4}+b)& =(\color{red}{-q}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{2}q+3b+3.\frac{3}{2}& \text{Uitwerken } \\ & =-bq-\frac{3}{2}q+3b+\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{8}{9})(a+\frac{18}{18})& =(\color{red}{q}+\color{orange}{\frac{8}{9}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aq+1q+\frac{8}{9}a+\frac{8}{9}.1& \text{Uitwerken } \\ & =aq+1q+\frac{8}{9}a+\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-10}{5}-x)(\frac{-19}{18}+p)& =(\color{red}{-x}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{19}{18}x-2p+2.\frac{19}{18}& \text{Uitwerken } \\ & =-px+\frac{19}{18}x-2p+\frac{38}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{19}{18}x-2p+\frac{19}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{10}-p)(\frac{-2}{14}-b)& =(\color{red}{-p}+\color{orange}{\frac{7}{5}}).(\color{green}{-b}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{7}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{7}p-\frac{7}{5}b-\frac{7}{5}.\frac{1}{7}& \text{Uitwerken } \\ & =bp+\frac{1}{7}p-\frac{7}{5}b-\frac{7}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{1}{7}p-\frac{7}{5}b-\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x+\frac{14}{18})(b-\frac{-13}{18})& =(\color{red}{x}+\color{orange}{\frac{7}{9}}).(\color{green}{b}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{7}{9})} . \color{green}{(b)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{13}{18}x+\frac{7}{9}b+\frac{7}{9}.\frac{13}{18}& \text{Uitwerken } \\ & =bx+\frac{13}{18}x+\frac{7}{9}b+\frac{91}{162} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-13 14:56:57
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