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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{12}{13}-q)(a-\frac{1}{11})& =(\color{red}{-q}+\color{orange}{\frac{12}{13}}).(\color{green}{a}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{12}{13})} . \color{green}{(a)} + \color{orange}{(\frac{12}{13})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{11}q+\frac{12}{13}a-\frac{12}{13}.\frac{1}{11}& \text{Uitwerken } \\ & =-aq+\frac{1}{11}q+\frac{12}{13}a-\frac{12}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{9}{16})(\frac{-18}{16}+a)& =(\color{red}{a}+\color{orange}{\frac{-9}{16}}).(\color{green}{a}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{9}{8}a-\frac{9}{16}a+\frac{9}{16}.\frac{9}{8}& \text{Uitwerken } \\ & =a^2+((\frac{-9}{8})+(\frac{-9}{16}))a+\frac{81}{128} & \text{Neem samen} \\ &=a^2-\frac{27}{16}a+\frac{81}{128} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{1}{9}+q)(\frac{-4}{7}-q)& =(\color{red}{q}+\color{orange}{\frac{1}{9}}).(\color{green}{-q}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{1}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{4}{7}q-\frac{1}{9}q-\frac{1}{9}.\frac{4}{7}& \text{Uitwerken } \\ & =-q^2+((\frac{-4}{7})+(\frac{-1}{9}))q-\frac{4}{63} & \text{Neem samen} \\ &=-q^2-\frac{43}{63}q-\frac{4}{63} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{8}{9}-q)(p-\frac{-6}{11})& =(\color{red}{-q}+\color{orange}{\frac{8}{9}}).(\color{green}{p}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{6}{11}q+\frac{8}{9}p+\frac{8}{9}.\frac{6}{11}& \text{Uitwerken } \\ & =-pq-\frac{6}{11}q+\frac{8}{9}p+\frac{48}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{6}{11}q+\frac{8}{9}p+\frac{16}{33} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{14}{15}+b)(\frac{20}{11}+b)& =(\color{red}{b}+\color{orange}{\frac{14}{15}}).(\color{green}{b}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{14}{15})} . \color{green}{(b)} + \color{orange}{(\frac{14}{15})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{20}{11}b+\frac{14}{15}b+\frac{14}{15}.\frac{20}{11}& \text{Uitwerken } \\ & =b^2+(\frac{20}{11}+\frac{14}{15})b+\frac{280}{165} & \text{Neem samen} \\ &=b^2+\frac{454}{165}b+\frac{280}{165} & \text{Maak de som} \\ &=b^2+\frac{454}{165}b+\frac{56}{33} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(q+\frac{9}{16})(\frac{14}{13}-a)& =(\color{red}{q}+\color{orange}{\frac{9}{16}}).(\color{green}{-a}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(\frac{9}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{14}{13}q-\frac{9}{16}a+\frac{9}{16}.\frac{14}{13}& \text{Uitwerken } \\ & =-aq+\frac{14}{13}q-\frac{9}{16}a+\frac{126}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{14}{13}q-\frac{9}{16}a+\frac{63}{104} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-4}{5})(p+\frac{3}{14})& =(\color{red}{q}+\color{orange}{\frac{-4}{5}}).(\color{green}{p}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{14}q-\frac{4}{5}p-\frac{4}{5}.\frac{3}{14}& \text{Uitwerken } \\ & =pq+\frac{3}{14}q-\frac{4}{5}p-\frac{12}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{3}{14}q-\frac{4}{5}p-\frac{6}{35} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{12}{13})((-7)-a)& =(\color{red}{p}+\color{orange}{\frac{12}{13}}).(\color{green}{-a}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(-7)} + \color{orange}{(\frac{12}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{12}{13})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = -ap-7p-\frac{12}{13}a-\frac{12}{13}.7& \text{Uitwerken } \\ & =-ap-7p-\frac{12}{13}a-\frac{84}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{20}{3})(\frac{12}{4}+x)& =(\color{red}{p}+\color{orange}{\frac{-20}{3}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{-20}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = px+3p-\frac{20}{3}x-\frac{20}{3}.3& \text{Uitwerken } \\ & =px+3p-\frac{20}{3}x-\frac{60}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+3p-\frac{20}{3}x-20 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-19}{9})(a-\frac{14}{16})& =(\color{red}{x}+\color{orange}{\frac{19}{9}}).(\color{green}{a}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{19}{9})} . \color{green}{(a)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{8}x+\frac{19}{9}a-\frac{19}{9}.\frac{7}{8}& \text{Uitwerken } \\ & =ax-\frac{7}{8}x+\frac{19}{9}a-\frac{133}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{7}{6})(\frac{3}{9}+q)& =(\color{red}{q}+\color{orange}{\frac{7}{6}}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{7}{6})} . \color{green}{(q)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{3}q+\frac{7}{6}q+\frac{7}{6}.\frac{1}{3}& \text{Uitwerken } \\ & =q^2+(\frac{1}{3}+\frac{7}{6})q+\frac{7}{18} & \text{Neem samen} \\ &=q^2+\frac{9}{6}q+\frac{7}{18} & \text{Maak de som} \\ &=q^2+\frac{3}{2}q+\frac{7}{18} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{-5}{18}-q)(\frac{19}{2}-a)& =(\color{red}{-q}+\color{orange}{\frac{-5}{18}}).(\color{green}{-a}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{2}q+\frac{5}{18}a-\frac{5}{18}.\frac{19}{2}& \text{Uitwerken } \\ & =aq-\frac{19}{2}q+\frac{5}{18}a-\frac{95}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-25 16:20:24
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