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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-3}{9}+x)(\frac{13}{19}-a)& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{-a}+\color{blue}{\frac{13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{13}{19})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{13}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{19}x+\frac{1}{3}a-\frac{1}{3}.\frac{13}{19}& \text{Uitwerken } \\ & =-ax+\frac{13}{19}x+\frac{1}{3}a-\frac{13}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-17}{8}-q)(x-\frac{-6}{5})& =(\color{red}{-q}+\color{orange}{\frac{-17}{8}}).(\color{green}{x}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-17}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{6}{5}q-\frac{17}{8}x-\frac{17}{8}.\frac{6}{5}& \text{Uitwerken } \\ & =-qx-\frac{6}{5}q-\frac{17}{8}x-\frac{102}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{6}{5}q-\frac{17}{8}x-\frac{51}{20} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-6}{4})(\frac{-4}{5}+p)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{5}b-\frac{3}{2}p+\frac{3}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =bp-\frac{4}{5}b-\frac{3}{2}p+\frac{12}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{4}{5}b-\frac{3}{2}p+\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-18}{9})(\frac{4}{2}+p)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2a+2p+2.2& \text{Uitwerken } \\ & =ap+2a+2p+4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-9}{10})(b+\frac{18}{3})& =(\color{red}{q}+\color{orange}{\frac{9}{10}}).(\color{green}{b}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(6)} + \color{orange}{(\frac{9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bq+6q+\frac{9}{10}b+\frac{9}{10}.6& \text{Uitwerken } \\ & =bq+6q+\frac{9}{10}b+\frac{54}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+6q+\frac{9}{10}b+\frac{27}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{6}{15}+p)(p+\frac{9}{5})& =(\color{red}{p}+\color{orange}{\frac{2}{5}}).(\color{green}{p}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{5}p+\frac{2}{5}p+\frac{2}{5}.\frac{9}{5}& \text{Uitwerken } \\ & =p^2+(\frac{9}{5}+\frac{2}{5})p+\frac{18}{25} & \text{Neem samen} \\ &=p^2+\frac{11}{5}p+\frac{18}{25} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-7}{17})(\frac{14}{13}+x)& =(\color{red}{b}+\color{orange}{\frac{-7}{17}}).(\color{green}{x}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{14}{13}b-\frac{7}{17}x-\frac{7}{17}.\frac{14}{13}& \text{Uitwerken } \\ & =bx+\frac{14}{13}b-\frac{7}{17}x-\frac{98}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-17}{6})(x+\frac{5}{8})& =(\color{red}{q}+\color{orange}{\frac{-17}{6}}).(\color{green}{x}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{8}q-\frac{17}{6}x-\frac{17}{6}.\frac{5}{8}& \text{Uitwerken } \\ & =qx+\frac{5}{8}q-\frac{17}{6}x-\frac{85}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{9}{16})(\frac{14}{6}-b)& =(\color{red}{b}+\color{orange}{\frac{-9}{16}}).(\color{green}{-b}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{7}{3}b+\frac{9}{16}b-\frac{9}{16}.\frac{7}{3}& \text{Uitwerken } \\ & =-b^2+(\frac{7}{3}+\frac{9}{16})b-\frac{63}{48} & \text{Neem samen} \\ &=-b^2+\frac{139}{48}b-\frac{63}{48} & \text{Maak de som} \\ &=-b^2+\frac{139}{48}b-\frac{21}{16} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-8}{12})(b-\frac{5}{8})& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{5}{8}b+\frac{2}{3}b-\frac{2}{3}.\frac{5}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-5}{8})+\frac{2}{3})b-(\frac{-10}{24}) & \text{Neem samen} \\ &=b^2+\frac{1}{24}b-(\frac{-10}{24}) & \text{Maak de som} \\ &=b^2+\frac{1}{24}b+\frac{5}{12} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(\frac{-15}{10}+p)(x+\frac{-13}{7})& =(\color{red}{p}+\color{orange}{\frac{-3}{2}}).(\color{green}{x}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{7}p-\frac{3}{2}x+\frac{3}{2}.\frac{13}{7}& \text{Uitwerken } \\ & =px-\frac{13}{7}p-\frac{3}{2}x+\frac{39}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{2}{5})(\frac{-5}{6}-b)& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{-b}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{6}x-\frac{2}{5}b-\frac{2}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =-bx-\frac{5}{6}x-\frac{2}{5}b-\frac{10}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{5}{6}x-\frac{2}{5}b-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
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