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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{5}{19}+b)(\frac{15}{14}-a)& =(\color{red}{b}+\color{orange}{\frac{5}{19}}).(\color{green}{-a}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{5}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{15}{14}b-\frac{5}{19}a+\frac{5}{19}.\frac{15}{14}& \text{Uitwerken } \\ & =-ab+\frac{15}{14}b-\frac{5}{19}a+\frac{75}{266} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{-10}{20})(p-\frac{-9}{2})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{2}x-\frac{1}{2}p-\frac{1}{2}.\frac{9}{2}& \text{Uitwerken } \\ & =px+\frac{9}{2}x-\frac{1}{2}p-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-10}{17}-x)(\frac{-2}{7}-b)& =(\color{red}{-x}+\color{orange}{\frac{-10}{17}}).(\color{green}{-b}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-10}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{7}x+\frac{10}{17}b+\frac{10}{17}.\frac{2}{7}& \text{Uitwerken } \\ & =bx+\frac{2}{7}x+\frac{10}{17}b+\frac{20}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{7}{12})(a+\frac{-8}{14})& =(\color{red}{q}+\color{orange}{\frac{-7}{12}}).(\color{green}{a}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{7}q-\frac{7}{12}a+\frac{7}{12}.\frac{4}{7}& \text{Uitwerken } \\ & =aq-\frac{4}{7}q-\frac{7}{12}a+\frac{28}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{4}{7}q-\frac{7}{12}a+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-12}{13}-b)(\frac{9}{6}+x)& =(\color{red}{-b}+\color{orange}{\frac{-12}{13}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{2}b-\frac{12}{13}x-\frac{12}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =-bx-\frac{3}{2}b-\frac{12}{13}x-\frac{36}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{3}{2}b-\frac{12}{13}x-\frac{18}{13} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{12}{17})(\frac{-8}{13}+q)& =(\color{red}{b}+\color{orange}{\frac{12}{17}}).(\color{green}{q}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{12}{17})} . \color{green}{(q)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{13}b+\frac{12}{17}q-\frac{12}{17}.\frac{8}{13}& \text{Uitwerken } \\ & =bq-\frac{8}{13}b+\frac{12}{17}q-\frac{96}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{19}{7}+p)(\frac{-19}{17}-b)& =(\color{red}{p}+\color{orange}{\frac{19}{7}}).(\color{green}{-b}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{19}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{19}{17}p-\frac{19}{7}b-\frac{19}{7}.\frac{19}{17}& \text{Uitwerken } \\ & =-bp-\frac{19}{17}p-\frac{19}{7}b-\frac{361}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{12}{12})(a-\frac{4}{9})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{4}{9}a-1a+1.\frac{4}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-4}{9})+(-1))a+\frac{4}{9} & \text{Neem samen} \\ &=a^2-\frac{13}{9}a+\frac{4}{9} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-20}{11}+q)(x-\frac{18}{15})& =(\color{red}{q}+\color{orange}{\frac{-20}{11}}).(\color{green}{x}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{6}{5}q-\frac{20}{11}x+\frac{20}{11}.\frac{6}{5}& \text{Uitwerken } \\ & =qx-\frac{6}{5}q-\frac{20}{11}x+\frac{120}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{6}{5}q-\frac{20}{11}x+\frac{24}{11} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-12}{10}+a)(\frac{-14}{14}+q)& =(\color{red}{a}+\color{orange}{\frac{-6}{5}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-6}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a-\frac{6}{5}q+\frac{6}{5}.1& \text{Uitwerken } \\ & =aq-1a-\frac{6}{5}q+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-7}{9})(\frac{7}{13}-x)& =(\color{red}{x}+\color{orange}{\frac{-7}{9}}).(\color{green}{-x}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{7}{13}x+\frac{7}{9}x-\frac{7}{9}.\frac{7}{13}& \text{Uitwerken } \\ & =-x^2+(\frac{7}{13}+\frac{7}{9})x-\frac{49}{117} & \text{Neem samen} \\ &=-x^2+\frac{154}{117}x-\frac{49}{117} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{4}{9}+q)(\frac{8}{14}-a)& =(\color{red}{q}+\color{orange}{\frac{4}{9}}).(\color{green}{-a}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{4}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{4}{7}q-\frac{4}{9}a+\frac{4}{9}.\frac{4}{7}& \text{Uitwerken } \\ & =-aq+\frac{4}{7}q-\frac{4}{9}a+\frac{16}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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