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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{18}{13}+a)(p-\frac{-16}{20})& =(\color{red}{a}+\color{orange}{\frac{18}{13}}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{18}{13})} . \color{green}{(p)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{5}a+\frac{18}{13}p+\frac{18}{13}.\frac{4}{5}& \text{Uitwerken } \\ & =ap+\frac{4}{5}a+\frac{18}{13}p+\frac{72}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{7}{6}+b)(a-\frac{17}{17})& =(\color{red}{b}+\color{orange}{\frac{7}{6}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{7}{6})} . \color{green}{(a)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1b+\frac{7}{6}a-\frac{7}{6}.1& \text{Uitwerken } \\ & =ab-1b+\frac{7}{6}a-\frac{7}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-9}{10}+a)(\frac{9}{8}-q)& =(\color{red}{a}+\color{orange}{\frac{-9}{10}}).(\color{green}{-q}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{8}a+\frac{9}{10}q-\frac{9}{10}.\frac{9}{8}& \text{Uitwerken } \\ & =-aq+\frac{9}{8}a+\frac{9}{10}q-\frac{81}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{13}+x)(b-(-6))& =(\color{red}{x}+\color{orange}{\frac{20}{13}}).(\color{green}{b}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(6)} + \color{orange}{(\frac{20}{13})} . \color{green}{(b)} + \color{orange}{(\frac{20}{13})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bx+6x+\frac{20}{13}b+\frac{20}{13}.6& \text{Uitwerken } \\ & =bx+6x+\frac{20}{13}b+\frac{120}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{20}{9}-p)(\frac{-2}{8}-p)& =(\color{red}{-p}+\color{orange}{\frac{20}{9}}).(\color{green}{-p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{20}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{4}p-\frac{20}{9}p-\frac{20}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =p^2+(\frac{1}{4}+(\frac{-20}{9}))p-(\frac{-20}{36}) & \text{Neem samen} \\ &=p^2-\frac{71}{36}p-(\frac{-20}{36}) & \text{Maak de som} \\ &=p^2-\frac{71}{36}p+\frac{5}{9} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(p-\frac{19}{12})(\frac{-8}{18}-a)& =(\color{red}{p}+\color{orange}{\frac{-19}{12}}).(\color{green}{-a}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{4}{9}p+\frac{19}{12}a+\frac{19}{12}.\frac{4}{9}& \text{Uitwerken } \\ & =-ap-\frac{4}{9}p+\frac{19}{12}a+\frac{76}{108} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{4}{9}p+\frac{19}{12}a+\frac{19}{27} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{7}+a)(\frac{-15}{2}-q)& =(\color{red}{a}+\color{orange}{\frac{8}{7}}).(\color{green}{-q}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{8}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{15}{2}a-\frac{8}{7}q-\frac{8}{7}.\frac{15}{2}& \text{Uitwerken } \\ & =-aq-\frac{15}{2}a-\frac{8}{7}q-\frac{120}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{15}{2}a-\frac{8}{7}q-\frac{60}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-2}{15})(x+\frac{-15}{9})& =(\color{red}{p}+\color{orange}{\frac{-2}{15}}).(\color{green}{x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{3}p-\frac{2}{15}x+\frac{2}{15}.\frac{5}{3}& \text{Uitwerken } \\ & =px-\frac{5}{3}p-\frac{2}{15}x+\frac{10}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{5}{3}p-\frac{2}{15}x+\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{7}{2})(\frac{-8}{13}-q)& =(\color{red}{p}+\color{orange}{\frac{-7}{2}}).(\color{green}{-q}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{8}{13}p+\frac{7}{2}q+\frac{7}{2}.\frac{8}{13}& \text{Uitwerken } \\ & =-pq-\frac{8}{13}p+\frac{7}{2}q+\frac{56}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{8}{13}p+\frac{7}{2}q+\frac{28}{13} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-10}{20}+a)(\frac{18}{16}-x)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{-x}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{8}a+\frac{1}{2}x-\frac{1}{2}.\frac{9}{8}& \text{Uitwerken } \\ & =-ax+\frac{9}{8}a+\frac{1}{2}x-\frac{9}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{9}{7})(\frac{-3}{17}+q)& =(\color{red}{a}+\color{orange}{\frac{-9}{7}}).(\color{green}{q}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{17}a-\frac{9}{7}q+\frac{9}{7}.\frac{3}{17}& \text{Uitwerken } \\ & =aq-\frac{3}{17}a-\frac{9}{7}q+\frac{27}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-14}{2})(\frac{20}{19}-x)& =(\color{red}{b}+\color{orange}{7}).(\color{green}{-x}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(7)} . \color{green}{(-x)} + \color{orange}{(7)} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{20}{19}b-7x+7.\frac{20}{19}& \text{Uitwerken } \\ & =-bx+\frac{20}{19}b-7x+\frac{140}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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