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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-3}{18})(x-\frac{11}{14})& =(\color{red}{x}+\color{orange}{\frac{1}{6}}).(\color{green}{x}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{11}{14}x+\frac{1}{6}x-\frac{1}{6}.\frac{11}{14}& \text{Uitwerken } \\ & =x^2+((\frac{-11}{14})+\frac{1}{6})x-(\frac{-11}{84}) & \text{Neem samen} \\ &=x^2-\frac{26}{42}x-(\frac{-11}{84}) & \text{Maak de som} \\ &=x^2-\frac{13}{21}x+\frac{11}{84} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(q-\frac{4}{2})(\frac{-1}{12}+a)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{12}q-2a+2.\frac{1}{12}& \text{Uitwerken } \\ & =aq-\frac{1}{12}q-2a+\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{12}q-2a+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-12}{7})(\frac{16}{18}+x)& =(\color{red}{a}+\color{orange}{\frac{12}{7}}).(\color{green}{x}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{12}{7})} . \color{green}{(x)} + \color{orange}{(\frac{12}{7})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{8}{9}a+\frac{12}{7}x+\frac{12}{7}.\frac{8}{9}& \text{Uitwerken } \\ & =ax+\frac{8}{9}a+\frac{12}{7}x+\frac{96}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{8}{9}a+\frac{12}{7}x+\frac{32}{21} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b-\frac{-15}{14})(a-\frac{-13}{14})& =(\color{red}{b}+\color{orange}{\frac{15}{14}}).(\color{green}{a}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{15}{14})} . \color{green}{(a)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{14}b+\frac{15}{14}a+\frac{15}{14}.\frac{13}{14}& \text{Uitwerken } \\ & =ab+\frac{13}{14}b+\frac{15}{14}a+\frac{195}{196} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{-5}{15})(\frac{5}{9}-b)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{-b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{9}x-\frac{1}{3}b+\frac{1}{3}.\frac{5}{9}& \text{Uitwerken } \\ & =-bx+\frac{5}{9}x-\frac{1}{3}b+\frac{5}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{3}{7}+q)(p+\frac{9}{7})& =(\color{red}{q}+\color{orange}{\frac{3}{7}}).(\color{green}{p}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{7}q+\frac{3}{7}p+\frac{3}{7}.\frac{9}{7}& \text{Uitwerken } \\ & =pq+\frac{9}{7}q+\frac{3}{7}p+\frac{27}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+(-1))(a-\frac{-1}{14})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{14}b-1a-1.\frac{1}{14}& \text{Uitwerken } \\ & =ab+\frac{1}{14}b-1a-\frac{1}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-13}{7})(p-\frac{-20}{19})& =(\color{red}{q}+\color{orange}{\frac{13}{7}}).(\color{green}{p}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{13}{7})} . \color{green}{(p)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{20}{19}q+\frac{13}{7}p+\frac{13}{7}.\frac{20}{19}& \text{Uitwerken } \\ & =pq+\frac{20}{19}q+\frac{13}{7}p+\frac{260}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-19}{4})(\frac{-2}{13}+p)& =(\color{red}{q}+\color{orange}{\frac{19}{4}}).(\color{green}{p}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{19}{4})} . \color{green}{(p)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{13}q+\frac{19}{4}p-\frac{19}{4}.\frac{2}{13}& \text{Uitwerken } \\ & =pq-\frac{2}{13}q+\frac{19}{4}p-\frac{38}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{2}{13}q+\frac{19}{4}p-\frac{19}{26} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{19}{15}-q)(\frac{-14}{11}+p)& =(\color{red}{-q}+\color{orange}{\frac{19}{15}}).(\color{green}{p}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{19}{15})} . \color{green}{(p)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{14}{11}q+\frac{19}{15}p-\frac{19}{15}.\frac{14}{11}& \text{Uitwerken } \\ & =-pq+\frac{14}{11}q+\frac{19}{15}p-\frac{266}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-15}{5}+q)(a-\frac{-8}{2})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(4)} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = aq+4q-3a-3.4& \text{Uitwerken } \\ & =aq+4q-3a-12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-9}{15}+x)(q+\frac{-8}{8})& =(\color{red}{x}+\color{orange}{\frac{-3}{5}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1x-\frac{3}{5}q+\frac{3}{5}.1& \text{Uitwerken } \\ & =qx-1x-\frac{3}{5}q+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-23 12:23:24
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