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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{1}{17}+q)(\frac{-1}{7}-p)& =(\color{red}{q}+\color{orange}{\frac{1}{17}}).(\color{green}{-p}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{1}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{7}q-\frac{1}{17}p-\frac{1}{17}.\frac{1}{7}& \text{Uitwerken } \\ & =-pq-\frac{1}{7}q-\frac{1}{17}p-\frac{1}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-9}{14}-b)(\frac{16}{4}+q)& =(\color{red}{-b}+\color{orange}{\frac{-9}{14}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(4)} + \color{orange}{(\frac{-9}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -bq-4b-\frac{9}{14}q-\frac{9}{14}.4& \text{Uitwerken } \\ & =-bq-4b-\frac{9}{14}q-\frac{36}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-4b-\frac{9}{14}q-\frac{18}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-6}{2}+x)(b+\frac{12}{9})& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{4}{3}x-3b-3.\frac{4}{3}& \text{Uitwerken } \\ & =bx+\frac{4}{3}x-3b-\frac{12}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{4}{3}x-3b-4 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q+\frac{11}{8})(a+\frac{-10}{11})& =(\color{red}{q}+\color{orange}{\frac{11}{8}}).(\color{green}{a}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{11}{8})} . \color{green}{(a)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{10}{11}q+\frac{11}{8}a-\frac{11}{8}.\frac{10}{11}& \text{Uitwerken } \\ & =aq-\frac{10}{11}q+\frac{11}{8}a-\frac{110}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{10}{11}q+\frac{11}{8}a-\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{3}+b)(q-\frac{19}{10})& =(\color{red}{b}+\color{orange}{\frac{16}{3}}).(\color{green}{q}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{16}{3})} . \color{green}{(q)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{10}b+\frac{16}{3}q-\frac{16}{3}.\frac{19}{10}& \text{Uitwerken } \\ & =bq-\frac{19}{10}b+\frac{16}{3}q-\frac{304}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{19}{10}b+\frac{16}{3}q-\frac{152}{15} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-4}{18})(\frac{5}{8}+a)& =(\color{red}{b}+\color{orange}{\frac{-2}{9}}).(\color{green}{a}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{8}b-\frac{2}{9}a-\frac{2}{9}.\frac{5}{8}& \text{Uitwerken } \\ & =ab+\frac{5}{8}b-\frac{2}{9}a-\frac{10}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{5}{8}b-\frac{2}{9}a-\frac{5}{36} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{12}{2}+a)(\frac{-15}{13}+q)& =(\color{red}{a}+\color{orange}{6}).(\color{green}{q}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(6)} . \color{green}{(q)} + \color{orange}{(6)} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{13}a+6q-6.\frac{15}{13}& \text{Uitwerken } \\ & =aq-\frac{15}{13}a+6q-\frac{90}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{19}{3}+x)(b-\frac{-19}{11})& =(\color{red}{x}+\color{orange}{\frac{19}{3}}).(\color{green}{b}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{19}{3})} . \color{green}{(b)} + \color{orange}{(\frac{19}{3})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{11}x+\frac{19}{3}b+\frac{19}{3}.\frac{19}{11}& \text{Uitwerken } \\ & =bx+\frac{19}{11}x+\frac{19}{3}b+\frac{361}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{2}{7}+x)(b+\frac{-2}{10})& =(\color{red}{x}+\color{orange}{\frac{2}{7}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{2}{7})} . \color{green}{(b)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{5}x+\frac{2}{7}b-\frac{2}{7}.\frac{1}{5}& \text{Uitwerken } \\ & =bx-\frac{1}{5}x+\frac{2}{7}b-\frac{2}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{19}{8}+a)(\frac{-5}{10}+b)& =(\color{red}{a}+\color{orange}{\frac{19}{8}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{19}{8})} . \color{green}{(b)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{2}a+\frac{19}{8}b-\frac{19}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =ab-\frac{1}{2}a+\frac{19}{8}b-\frac{19}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-9}{8}+b)(q-\frac{15}{8})& =(\color{red}{b}+\color{orange}{\frac{-9}{8}}).(\color{green}{q}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{15}{8}b-\frac{9}{8}q+\frac{9}{8}.\frac{15}{8}& \text{Uitwerken } \\ & =bq-\frac{15}{8}b-\frac{9}{8}q+\frac{135}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-11}{12})(\frac{9}{10}-a)& =(\color{red}{a}+\color{orange}{\frac{11}{12}}).(\color{green}{-a}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{11}{12})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{12})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{9}{10}a-\frac{11}{12}a+\frac{11}{12}.\frac{9}{10}& \text{Uitwerken } \\ & =-a^2+(\frac{9}{10}+(\frac{-11}{12}))a+(\frac{-99}{120}) & \text{Neem samen} \\ &=-a^2-\frac{1}{60}a+(\frac{-99}{120}) & \text{Maak de som} \\ &=-a^2-\frac{1}{60}a+(\frac{-33}{40}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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