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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{11}{9})(\frac{10}{4}+q)& =(\color{red}{b}+\color{orange}{\frac{-11}{9}}).(\color{green}{q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{2}b-\frac{11}{9}q-\frac{11}{9}.\frac{5}{2}& \text{Uitwerken } \\ & =bq+\frac{5}{2}b-\frac{11}{9}q-\frac{55}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-16}{9})(x+\frac{-8}{14})& =(\color{red}{p}+\color{orange}{\frac{-16}{9}}).(\color{green}{x}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{7}p-\frac{16}{9}x+\frac{16}{9}.\frac{4}{7}& \text{Uitwerken } \\ & =px-\frac{4}{7}p-\frac{16}{9}x+\frac{64}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{14}{13}+b)(\frac{19}{4}-p)& =(\color{red}{b}+\color{orange}{\frac{14}{13}}).(\color{green}{-p}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{14}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{19}{4}b-\frac{14}{13}p+\frac{14}{13}.\frac{19}{4}& \text{Uitwerken } \\ & =-bp+\frac{19}{4}b-\frac{14}{13}p+\frac{266}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{19}{4}b-\frac{14}{13}p+\frac{133}{26} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-2}{10})(\frac{6}{8}+x)& =(\color{red}{p}+\color{orange}{\frac{-1}{5}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{4}p-\frac{1}{5}x-\frac{1}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =px+\frac{3}{4}p-\frac{1}{5}x-\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-18}{14})(b+\frac{-11}{20})& =(\color{red}{a}+\color{orange}{\frac{9}{7}}).(\color{green}{b}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{20}a+\frac{9}{7}b-\frac{9}{7}.\frac{11}{20}& \text{Uitwerken } \\ & =ab-\frac{11}{20}a+\frac{9}{7}b-\frac{99}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-14}{4})(p+\frac{-6}{13})& =(\color{red}{x}+\color{orange}{\frac{7}{2}}).(\color{green}{p}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{7}{2})} . \color{green}{(p)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{6}{13}x+\frac{7}{2}p-\frac{7}{2}.\frac{6}{13}& \text{Uitwerken } \\ & =px-\frac{6}{13}x+\frac{7}{2}p-\frac{42}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{6}{13}x+\frac{7}{2}p-\frac{21}{13} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(4+p)(b+\frac{-6}{19})& =(\color{red}{p}+\color{orange}{4}).(\color{green}{b}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(4)} . \color{green}{(b)} + \color{orange}{(4)} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{19}p+4b-4.\frac{6}{19}& \text{Uitwerken } \\ & =bp-\frac{6}{19}p+4b-\frac{24}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-7}{2})(q+\frac{18}{20})& =(\color{red}{x}+\color{orange}{\frac{-7}{2}}).(\color{green}{q}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{10}x-\frac{7}{2}q-\frac{7}{2}.\frac{9}{10}& \text{Uitwerken } \\ & =qx+\frac{9}{10}x-\frac{7}{2}q-\frac{63}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-18}{20})(b+\frac{9}{7})& =(\color{red}{q}+\color{orange}{\frac{9}{10}}).(\color{green}{b}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{7}q+\frac{9}{10}b+\frac{9}{10}.\frac{9}{7}& \text{Uitwerken } \\ & =bq+\frac{9}{7}q+\frac{9}{10}b+\frac{81}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{7}{17}-p)(q-\frac{-9}{17})& =(\color{red}{-p}+\color{orange}{\frac{7}{17}}).(\color{green}{q}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{7}{17})} . \color{green}{(q)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{17}p+\frac{7}{17}q+\frac{7}{17}.\frac{9}{17}& \text{Uitwerken } \\ & =-pq-\frac{9}{17}p+\frac{7}{17}q+\frac{63}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{18}+x)(a-\frac{-15}{5})& =(\color{red}{x}+\color{orange}{\frac{2}{9}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{2}{9})} . \color{green}{(a)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ax+3x+\frac{2}{9}a+\frac{2}{9}.3& \text{Uitwerken } \\ & =ax+3x+\frac{2}{9}a+\frac{6}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+3x+\frac{2}{9}a+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x-(-9))(\frac{11}{5}-x)& =(\color{red}{x}+\color{orange}{9}).(\color{green}{-x}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(9)} . \color{green}{(-x)} + \color{orange}{(9)} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{11}{5}x-9x+9.\frac{11}{5}& \text{Uitwerken } \\ & =-x^2+(\frac{11}{5}+(-9))x+(\frac{-99}{5}) & \text{Neem samen} \\ &=-x^2-\frac{34}{5}x+(\frac{-99}{5}) & \text{Maak de som} \\\end{align}\)
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