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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{4}+p)(a-\frac{6}{3})& =(\color{red}{p}+\color{orange}{\frac{9}{4}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ap-2p+\frac{9}{4}a-\frac{9}{4}.2& \text{Uitwerken } \\ & =ap-2p+\frac{9}{4}a-\frac{18}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-2p+\frac{9}{4}a-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{6}{20}+b)(\frac{-2}{4}+p)& =(\color{red}{b}+\color{orange}{\frac{3}{10}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{2}b+\frac{3}{10}p-\frac{3}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =bp-\frac{1}{2}b+\frac{3}{10}p-\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{17}+a)(p+\frac{-18}{5})& =(\color{red}{a}+\color{orange}{\frac{-16}{17}}).(\color{green}{p}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{18}{5}a-\frac{16}{17}p+\frac{16}{17}.\frac{18}{5}& \text{Uitwerken } \\ & =ap-\frac{18}{5}a-\frac{16}{17}p+\frac{288}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{3}{10})(\frac{-13}{17}+q)& =(\color{red}{q}+\color{orange}{\frac{3}{10}}).(\color{green}{q}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{13}{17}q+\frac{3}{10}q-\frac{3}{10}.\frac{13}{17}& \text{Uitwerken } \\ & =q^2+((\frac{-13}{17})+\frac{3}{10})q-(\frac{-39}{170}) & \text{Neem samen} \\ &=q^2-\frac{79}{170}q-(\frac{-39}{170}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-3}{2}-q)(q+\frac{-17}{7})& =(\color{red}{-q}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{17}{7}q-\frac{3}{2}q+\frac{3}{2}.\frac{17}{7}& \text{Uitwerken } \\ & =-q^2+(\frac{17}{7}+(\frac{-3}{2}))q+(\frac{-51}{14}) & \text{Neem samen} \\ &=-q^2+\frac{13}{14}q+(\frac{-51}{14}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{15}{14}-a)(p-\frac{6}{19})& =(\color{red}{-a}+\color{orange}{\frac{15}{14}}).(\color{green}{p}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{15}{14})} . \color{green}{(p)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{6}{19}a+\frac{15}{14}p-\frac{15}{14}.\frac{6}{19}& \text{Uitwerken } \\ & =-ap+\frac{6}{19}a+\frac{15}{14}p-\frac{90}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{6}{19}a+\frac{15}{14}p-\frac{45}{133} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q-\frac{16}{14})(\frac{14}{13}-q)& =(\color{red}{q}+\color{orange}{\frac{-8}{7}}).(\color{green}{-q}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{14}{13}q+\frac{8}{7}q-\frac{8}{7}.\frac{14}{13}& \text{Uitwerken } \\ & =-q^2+(\frac{14}{13}+\frac{8}{7})q-\frac{112}{91} & \text{Neem samen} \\ &=-q^2+\frac{202}{91}q-\frac{112}{91} & \text{Maak de som} \\ &=-q^2+\frac{202}{91}q-\frac{16}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(x-\frac{8}{5})(a+\frac{-17}{5})& =(\color{red}{x}+\color{orange}{\frac{-8}{5}}).(\color{green}{a}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{5}x-\frac{8}{5}a+\frac{8}{5}.\frac{17}{5}& \text{Uitwerken } \\ & =ax-\frac{17}{5}x-\frac{8}{5}a+\frac{136}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-19}{5})(\frac{18}{12}-b)& =(\color{red}{a}+\color{orange}{\frac{19}{5}}).(\color{green}{-b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{19}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{5})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{2}a-\frac{19}{5}b+\frac{19}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =-ab+\frac{3}{2}a-\frac{19}{5}b+\frac{57}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{11}{20})(\frac{19}{3}-x)& =(\color{red}{a}+\color{orange}{\frac{11}{20}}).(\color{green}{-x}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{11}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{19}{3}a-\frac{11}{20}x+\frac{11}{20}.\frac{19}{3}& \text{Uitwerken } \\ & =-ax+\frac{19}{3}a-\frac{11}{20}x+\frac{209}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+14)(\frac{-4}{7}-a)& =(\color{red}{a}+\color{orange}{14}).(\color{green}{-a}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(14)} . \color{green}{(-a)} + \color{orange}{(14)} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{4}{7}a-14a-14.\frac{4}{7}& \text{Uitwerken } \\ & =-a^2+((\frac{-4}{7})+(-14))a-\frac{56}{7} & \text{Neem samen} \\ &=-a^2-\frac{102}{7}a-\frac{56}{7} & \text{Maak de som} \\ &=-a^2-\frac{102}{7}a-8 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(x+\frac{9}{19})(\frac{8}{19}+q)& =(\color{red}{x}+\color{orange}{\frac{9}{19}}).(\color{green}{q}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{9}{19})} . \color{green}{(q)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{8}{19}x+\frac{9}{19}q+\frac{9}{19}.\frac{8}{19}& \text{Uitwerken } \\ & =qx+\frac{8}{19}x+\frac{9}{19}q+\frac{72}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-09 19:58:16
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