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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{14}-x)(\frac{-19}{10}-x)& =(\color{red}{-x}+\color{orange}{\frac{15}{14}}).(\color{green}{-x}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{15}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{19}{10}x-\frac{15}{14}x-\frac{15}{14}.\frac{19}{10}& \text{Uitwerken } \\ & =x^2+(\frac{19}{10}+(\frac{-15}{14}))x-(\frac{-285}{140}) & \text{Neem samen} \\ &=x^2+\frac{58}{70}x-(\frac{-285}{140}) & \text{Maak de som} \\ &=x^2+\frac{29}{35}x+\frac{57}{28} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(b-\frac{5}{15})(p+\frac{16}{15})& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{p}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{16}{15}b-\frac{1}{3}p-\frac{1}{3}.\frac{16}{15}& \text{Uitwerken } \\ & =bp+\frac{16}{15}b-\frac{1}{3}p-\frac{16}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-16}{17})(p-\frac{9}{14})& =(\color{red}{a}+\color{orange}{\frac{-16}{17}}).(\color{green}{p}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{14}a-\frac{16}{17}p+\frac{16}{17}.\frac{9}{14}& \text{Uitwerken } \\ & =ap-\frac{9}{14}a-\frac{16}{17}p+\frac{144}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{9}{14}a-\frac{16}{17}p+\frac{72}{119} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-4}{7})(\frac{-8}{18}-b)& =(\color{red}{x}+\color{orange}{\frac{4}{7}}).(\color{green}{-b}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{4}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{9}x-\frac{4}{7}b-\frac{4}{7}.\frac{4}{9}& \text{Uitwerken } \\ & =-bx-\frac{4}{9}x-\frac{4}{7}b-\frac{16}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{11}{3}-q)(x-\frac{1}{4})& =(\color{red}{-q}+\color{orange}{\frac{11}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{11}{3})} . \color{green}{(x)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{4}q+\frac{11}{3}x-\frac{11}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =-qx+\frac{1}{4}q+\frac{11}{3}x-\frac{11}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{17}{14})(\frac{20}{18}+q)& =(\color{red}{b}+\color{orange}{\frac{-17}{14}}).(\color{green}{q}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{10}{9}b-\frac{17}{14}q-\frac{17}{14}.\frac{10}{9}& \text{Uitwerken } \\ & =bq+\frac{10}{9}b-\frac{17}{14}q-\frac{170}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{10}{9}b-\frac{17}{14}q-\frac{85}{63} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+(-1))(x-\frac{-8}{20})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{2}{5}p-1x-1.\frac{2}{5}& \text{Uitwerken } \\ & =px+\frac{2}{5}p-1x-\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{19}{3})(\frac{-1}{17}-q)& =(\color{red}{p}+\color{orange}{\frac{19}{3}}).(\color{green}{-q}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{19}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{3})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{17}p-\frac{19}{3}q-\frac{19}{3}.\frac{1}{17}& \text{Uitwerken } \\ & =-pq-\frac{1}{17}p-\frac{19}{3}q-\frac{19}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-14}{6}+p)(\frac{-20}{3}-p)& =(\color{red}{p}+\color{orange}{\frac{-7}{3}}).(\color{green}{-p}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{20}{3}p+\frac{7}{3}p+\frac{7}{3}.\frac{20}{3}& \text{Uitwerken } \\ & =-p^2+((\frac{-20}{3})+\frac{7}{3})p+(\frac{-140}{9}) & \text{Neem samen} \\ &=-p^2-\frac{13}{3}p+(\frac{-140}{9}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-13}{7}-p)(\frac{19}{10}-a)& =(\color{red}{-p}+\color{orange}{\frac{-13}{7}}).(\color{green}{-a}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{10}p+\frac{13}{7}a-\frac{13}{7}.\frac{19}{10}& \text{Uitwerken } \\ & =ap-\frac{19}{10}p+\frac{13}{7}a-\frac{247}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-20}{10})(\frac{-4}{17}-p)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{4}{17}x+2p+2.\frac{4}{17}& \text{Uitwerken } \\ & =-px-\frac{4}{17}x+2p+\frac{8}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{14}{12})(p-2)& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ap-2a-\frac{7}{6}p+\frac{7}{6}.2& \text{Uitwerken } \\ & =ap-2a-\frac{7}{6}p+\frac{14}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-2a-\frac{7}{6}p+\frac{7}{3} & \text{Vereenvoudig} \\\end{align}\)
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