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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{2}{19}-x)(a+\frac{7}{8})& =(\color{red}{-x}+\color{orange}{\frac{2}{19}}).(\color{green}{a}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{2}{19})} . \color{green}{(a)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{7}{8}x+\frac{2}{19}a+\frac{2}{19}.\frac{7}{8}& \text{Uitwerken } \\ & =-ax-\frac{7}{8}x+\frac{2}{19}a+\frac{14}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{7}{8}x+\frac{2}{19}a+\frac{7}{76} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-17}{18}+p)(\frac{-19}{7}-p)& =(\color{red}{p}+\color{orange}{\frac{-17}{18}}).(\color{green}{-p}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{19}{7}p+\frac{17}{18}p+\frac{17}{18}.\frac{19}{7}& \text{Uitwerken } \\ & =-p^2+((\frac{-19}{7})+\frac{17}{18})p+(\frac{-323}{126}) & \text{Neem samen} \\ &=-p^2-\frac{223}{126}p+(\frac{-323}{126}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{15}{3}+q)(p+\frac{-11}{6})& =(\color{red}{q}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{6}q+5p-5.\frac{11}{6}& \text{Uitwerken } \\ & =pq-\frac{11}{6}q+5p-\frac{55}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-10}{4})(\frac{-10}{2}-p)& =(\color{red}{p}+\color{orange}{\frac{-5}{2}}).(\color{green}{-p}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -pp-5p+\frac{5}{2}p+\frac{5}{2}.5& \text{Uitwerken } \\ & =-p^2+((-5)+\frac{5}{2})p+(\frac{-25}{2}) & \text{Neem samen} \\ &=-p^2-\frac{5}{2}p+(\frac{-25}{2}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{18}{11}-x)(\frac{5}{18}+b)& =(\color{red}{-x}+\color{orange}{\frac{18}{11}}).(\color{green}{b}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(\frac{18}{11})} . \color{green}{(b)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{18}x+\frac{18}{11}b+\frac{18}{11}.\frac{5}{18}& \text{Uitwerken } \\ & =-bx-\frac{5}{18}x+\frac{18}{11}b+\frac{90}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{5}{18}x+\frac{18}{11}b+\frac{5}{11} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{3}{19}+a)(\frac{-5}{2}+a)& =(\color{red}{a}+\color{orange}{\frac{3}{19}}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{3}{19})} . \color{green}{(a)} + \color{orange}{(\frac{3}{19})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{2}a+\frac{3}{19}a-\frac{3}{19}.\frac{5}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{2})+\frac{3}{19})a-(\frac{-15}{38}) & \text{Neem samen} \\ &=a^2-\frac{89}{38}a-(\frac{-15}{38}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b+\frac{10}{12})((-13)+p)& =(\color{red}{b}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{(-13)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-13)} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = bp-13b+\frac{5}{6}p-\frac{5}{6}.13& \text{Uitwerken } \\ & =bp-13b+\frac{5}{6}p-\frac{65}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{15}{13}+x)((-4)-a)& =(\color{red}{x}+\color{orange}{\frac{15}{13}}).(\color{green}{-a}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{15}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ax-4x-\frac{15}{13}a-\frac{15}{13}.4& \text{Uitwerken } \\ & =-ax-4x-\frac{15}{13}a-\frac{60}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{10}{19}+p)(q-\frac{-18}{3})& =(\color{red}{p}+\color{orange}{\frac{10}{19}}).(\color{green}{q}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(6)} + \color{orange}{(\frac{10}{19})} . \color{green}{(q)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = pq+6p+\frac{10}{19}q+\frac{10}{19}.6& \text{Uitwerken } \\ & =pq+6p+\frac{10}{19}q+\frac{60}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-19}{9})(p+\frac{10}{20})& =(\color{red}{q}+\color{orange}{\frac{-19}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{2}q-\frac{19}{9}p-\frac{19}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =pq+\frac{1}{2}q-\frac{19}{9}p-\frac{19}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{14}-q)(\frac{-4}{18}-q)& =(\color{red}{-q}+\color{orange}{\frac{-19}{14}}).(\color{green}{-q}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{2}{9}q+\frac{19}{14}q+\frac{19}{14}.\frac{2}{9}& \text{Uitwerken } \\ & =q^2+(\frac{2}{9}+\frac{19}{14})q+\frac{38}{126} & \text{Neem samen} \\ &=q^2+\frac{199}{126}q+\frac{38}{126} & \text{Maak de som} \\ &=q^2+\frac{199}{126}q+\frac{19}{63} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{-14}{20}-b)(\frac{-10}{15}+a)& =(\color{red}{-b}+\color{orange}{\frac{-7}{10}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{2}{3}b-\frac{7}{10}a+\frac{7}{10}.\frac{2}{3}& \text{Uitwerken } \\ & =-ab+\frac{2}{3}b-\frac{7}{10}a+\frac{14}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{2}{3}b-\frac{7}{10}a+\frac{7}{15} & \text{Vereenvoudig} \\\end{align}\)
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