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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{19}{18}-b)(q-\frac{3}{14})& =(\color{red}{-b}+\color{orange}{\frac{19}{18}}).(\color{green}{q}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{19}{18})} . \color{green}{(q)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{14}b+\frac{19}{18}q-\frac{19}{18}.\frac{3}{14}& \text{Uitwerken } \\ & =-bq+\frac{3}{14}b+\frac{19}{18}q-\frac{57}{252} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{3}{14}b+\frac{19}{18}q-\frac{19}{84} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-7}{15})(x-\frac{-6}{15})& =(\color{red}{a}+\color{orange}{\frac{7}{15}}).(\color{green}{x}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{7}{15})} . \color{green}{(x)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{5}a+\frac{7}{15}x+\frac{7}{15}.\frac{2}{5}& \text{Uitwerken } \\ & =ax+\frac{2}{5}a+\frac{7}{15}x+\frac{14}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{13}{13})(q+\frac{19}{9})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{19}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{19}{9})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{19}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{9}a+1q+1.\frac{19}{9}& \text{Uitwerken } \\ & =aq+\frac{19}{9}a+1q+\frac{19}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{5}{20}-b)(\frac{20}{18}+x)& =(\color{red}{-b}+\color{orange}{\frac{1}{4}}).(\color{green}{x}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{10}{9}b+\frac{1}{4}x+\frac{1}{4}.\frac{10}{9}& \text{Uitwerken } \\ & =-bx-\frac{10}{9}b+\frac{1}{4}x+\frac{10}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{10}{9}b+\frac{1}{4}x+\frac{5}{18} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-1}{9})(x-\frac{9}{15})& =(\color{red}{a}+\color{orange}{\frac{-1}{9}}).(\color{green}{x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{5}a-\frac{1}{9}x+\frac{1}{9}.\frac{3}{5}& \text{Uitwerken } \\ & =ax-\frac{3}{5}a-\frac{1}{9}x+\frac{3}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{3}{5}a-\frac{1}{9}x+\frac{1}{15} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{4}{20}+x)(q-\frac{-16}{10})& =(\color{red}{x}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{8}{5}x+\frac{1}{5}q+\frac{1}{5}.\frac{8}{5}& \text{Uitwerken } \\ & =qx+\frac{8}{5}x+\frac{1}{5}q+\frac{8}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{12}-q)(b+\frac{10}{4})& =(\color{red}{-q}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{2}q+\frac{2}{3}b+\frac{2}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =-bq-\frac{5}{2}q+\frac{2}{3}b+\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{5}{2}q+\frac{2}{3}b+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-17}{13})(\frac{15}{3}+q)& =(\color{red}{x}+\color{orange}{\frac{17}{13}}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(5)} + \color{orange}{(\frac{17}{13})} . \color{green}{(q)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = qx+5x+\frac{17}{13}q+\frac{17}{13}.5& \text{Uitwerken } \\ & =qx+5x+\frac{17}{13}q+\frac{85}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{8}{18})(\frac{-12}{16}-a)& =(\color{red}{a}+\color{orange}{\frac{-4}{9}}).(\color{green}{-a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{3}{4}a+\frac{4}{9}a+\frac{4}{9}.\frac{3}{4}& \text{Uitwerken } \\ & =-a^2+((\frac{-3}{4})+\frac{4}{9})a+(\frac{-12}{36}) & \text{Neem samen} \\ &=-a^2-\frac{11}{36}a+(\frac{-12}{36}) & \text{Maak de som} \\ &=-a^2-\frac{11}{36}a+(\frac{-1}{3}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(q+\frac{9}{12})(\frac{-14}{18}+b)& =(\color{red}{q}+\color{orange}{\frac{3}{4}}).(\color{green}{b}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{9}q+\frac{3}{4}b-\frac{3}{4}.\frac{7}{9}& \text{Uitwerken } \\ & =bq-\frac{7}{9}q+\frac{3}{4}b-\frac{21}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{7}{9}q+\frac{3}{4}b-\frac{7}{12} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{7}+x)(\frac{-7}{8}-q)& =(\color{red}{x}+\color{orange}{\frac{16}{7}}).(\color{green}{-q}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{16}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{7}{8}x-\frac{16}{7}q-\frac{16}{7}.\frac{7}{8}& \text{Uitwerken } \\ & =-qx-\frac{7}{8}x-\frac{16}{7}q-\frac{112}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{7}{8}x-\frac{16}{7}q-2 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{2}{13}+q)(\frac{20}{2}-q)& =(\color{red}{q}+\color{orange}{\frac{2}{13}}).(\color{green}{-q}+\color{blue}{10})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(10)} + \color{orange}{(\frac{2}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -qq+10q-\frac{2}{13}q+\frac{2}{13}.10& \text{Uitwerken } \\ & =-q^2+(10+(\frac{-2}{13}))q+(\frac{-20}{13}) & \text{Neem samen} \\ &=-q^2+\frac{128}{13}q+(\frac{-20}{13}) & \text{Maak de som} \\\end{align}\)
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