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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{20}-q)(\frac{13}{5}+x)& =(\color{red}{-q}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{5}q+\frac{3}{4}x+\frac{3}{4}.\frac{13}{5}& \text{Uitwerken } \\ & =-qx-\frac{13}{5}q+\frac{3}{4}x+\frac{39}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{13}{12}+a)(p+(-11))& =(\color{red}{a}+\color{orange}{\frac{13}{12}}).(\color{green}{p}+\color{blue}{(-11)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-11)} + \color{orange}{(\frac{13}{12})} . \color{green}{(p)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = ap-11a+\frac{13}{12}p-\frac{13}{12}.11& \text{Uitwerken } \\ & =ap-11a+\frac{13}{12}p-\frac{143}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-13}{20}+x)(\frac{12}{5}-x)& =(\color{red}{x}+\color{orange}{\frac{-13}{20}}).(\color{green}{-x}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{12}{5}x+\frac{13}{20}x-\frac{13}{20}.\frac{12}{5}& \text{Uitwerken } \\ & =-x^2+(\frac{12}{5}+\frac{13}{20})x-\frac{156}{100} & \text{Neem samen} \\ &=-x^2+\frac{61}{20}x-\frac{156}{100} & \text{Maak de som} \\ &=-x^2+\frac{61}{20}x-\frac{39}{25} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(a+\frac{18}{18})(a+\frac{-15}{19})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{15}{19}a+1a-1.\frac{15}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-15}{19})+1)a-(\frac{-15}{19}) & \text{Neem samen} \\ &=a^2+\frac{4}{19}a-(\frac{-15}{19}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{6}+q)(\frac{18}{4}-q)& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{-q}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{9}{2}q+\frac{3}{2}q-\frac{3}{2}.\frac{9}{2}& \text{Uitwerken } \\ & =-q^2+(\frac{9}{2}+\frac{3}{2})q-\frac{27}{4} & \text{Neem samen} \\ &=-q^2+\frac{12}{2}q-\frac{27}{4} & \text{Maak de som} \\ &=-q^2+6q-\frac{27}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(b-\frac{16}{14})(x+\frac{10}{12})& =(\color{red}{b}+\color{orange}{\frac{-8}{7}}).(\color{green}{x}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{6}b-\frac{8}{7}x-\frac{8}{7}.\frac{5}{6}& \text{Uitwerken } \\ & =bx+\frac{5}{6}b-\frac{8}{7}x-\frac{40}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{5}{6}b-\frac{8}{7}x-\frac{20}{21} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{16}{11}-x)(\frac{13}{2}-p)& =(\color{red}{-x}+\color{orange}{\frac{16}{11}}).(\color{green}{-p}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{16}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{2}x-\frac{16}{11}p+\frac{16}{11}.\frac{13}{2}& \text{Uitwerken } \\ & =px-\frac{13}{2}x-\frac{16}{11}p+\frac{208}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{13}{2}x-\frac{16}{11}p+\frac{104}{11} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q+13)(a+\frac{-11}{18})& =(\color{red}{q}+\color{orange}{13}).(\color{green}{a}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(13)} . \color{green}{(a)} + \color{orange}{(13)} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{18}q+13a-13.\frac{11}{18}& \text{Uitwerken } \\ & =aq-\frac{11}{18}q+13a-\frac{143}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{1}{9})(\frac{3}{10}+p)& =(\color{red}{a}+\color{orange}{\frac{1}{9}}).(\color{green}{p}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{10}a+\frac{1}{9}p+\frac{1}{9}.\frac{3}{10}& \text{Uitwerken } \\ & =ap+\frac{3}{10}a+\frac{1}{9}p+\frac{3}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{10}a+\frac{1}{9}p+\frac{1}{30} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-8}{6}-q)(p+\frac{15}{3})& =(\color{red}{-q}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(5)} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -pq-5q-\frac{4}{3}p-\frac{4}{3}.5& \text{Uitwerken } \\ & =-pq-5q-\frac{4}{3}p-\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-5}{13}+p)(a-\frac{14}{8})& =(\color{red}{p}+\color{orange}{\frac{-5}{13}}).(\color{green}{a}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{4}p-\frac{5}{13}a+\frac{5}{13}.\frac{7}{4}& \text{Uitwerken } \\ & =ap-\frac{7}{4}p-\frac{5}{13}a+\frac{35}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{2}{14}+b)(p-\frac{-12}{3})& =(\color{red}{b}+\color{orange}{\frac{1}{7}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(4)} + \color{orange}{(\frac{1}{7})} . \color{green}{(p)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bp+4b+\frac{1}{7}p+\frac{1}{7}.4& \text{Uitwerken } \\ & =bp+4b+\frac{1}{7}p+\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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