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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{2}{17})(\frac{-4}{12}+b)& =(\color{red}{q}+\color{orange}{\frac{-2}{17}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{3}q-\frac{2}{17}b+\frac{2}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =bq-\frac{1}{3}q-\frac{2}{17}b+\frac{2}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{7}{8}-q)(p+\frac{-1}{6})& =(\color{red}{-q}+\color{orange}{\frac{7}{8}}).(\color{green}{p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{6}q+\frac{7}{8}p-\frac{7}{8}.\frac{1}{6}& \text{Uitwerken } \\ & =-pq+\frac{1}{6}q+\frac{7}{8}p-\frac{7}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{9}{2}-b)(b+\frac{-11}{2})& =(\color{red}{-b}+\color{orange}{\frac{9}{2}}).(\color{green}{b}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{9}{2})} . \color{green}{(b)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{11}{2}b+\frac{9}{2}b-\frac{9}{2}.\frac{11}{2}& \text{Uitwerken } \\ & =-b^2+(\frac{11}{2}+\frac{9}{2})b-\frac{99}{4} & \text{Neem samen} \\ &=-b^2+\frac{20}{2}b-\frac{99}{4} & \text{Maak de som} \\ &=-b^2+10b-\frac{99}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(b-\frac{8}{17})(\frac{1}{17}-x)& =(\color{red}{b}+\color{orange}{\frac{-8}{17}}).(\color{green}{-x}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{17}b+\frac{8}{17}x-\frac{8}{17}.\frac{1}{17}& \text{Uitwerken } \\ & =-bx+\frac{1}{17}b+\frac{8}{17}x-\frac{8}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{2}{5})(\frac{-9}{10}+p)& =(\color{red}{b}+\color{orange}{\frac{2}{5}}).(\color{green}{p}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{10}b+\frac{2}{5}p-\frac{2}{5}.\frac{9}{10}& \text{Uitwerken } \\ & =bp-\frac{9}{10}b+\frac{2}{5}p-\frac{18}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{9}{10}b+\frac{2}{5}p-\frac{9}{25} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-18}{17})(\frac{-12}{2}+b)& =(\color{red}{a}+\color{orange}{\frac{-18}{17}}).(\color{green}{b}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-6)} + \color{orange}{(\frac{-18}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ab-6a-\frac{18}{17}b+\frac{18}{17}.6& \text{Uitwerken } \\ & =ab-6a-\frac{18}{17}b+\frac{108}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-10}{7}-x)(\frac{-12}{8}-a)& =(\color{red}{-x}+\color{orange}{\frac{-10}{7}}).(\color{green}{-a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{2}x+\frac{10}{7}a+\frac{10}{7}.\frac{3}{2}& \text{Uitwerken } \\ & =ax+\frac{3}{2}x+\frac{10}{7}a+\frac{30}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{2}x+\frac{10}{7}a+\frac{15}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{16}{17}-a)(b-\frac{10}{18})& =(\color{red}{-a}+\color{orange}{\frac{16}{17}}).(\color{green}{b}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{16}{17})} . \color{green}{(b)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{9}a+\frac{16}{17}b-\frac{16}{17}.\frac{5}{9}& \text{Uitwerken } \\ & =-ab+\frac{5}{9}a+\frac{16}{17}b-\frac{80}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-14}{14}-a)(a+\frac{1}{11})& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{1}{11}a-1a-1.\frac{1}{11}& \text{Uitwerken } \\ & =-a^2+((\frac{-1}{11})+(-1))a-\frac{1}{11} & \text{Neem samen} \\ &=-a^2-\frac{12}{11}a-\frac{1}{11} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-20}{3})(\frac{-9}{7}+x)& =(\color{red}{b}+\color{orange}{\frac{20}{3}}).(\color{green}{x}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{20}{3})} . \color{green}{(x)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{7}b+\frac{20}{3}x-\frac{20}{3}.\frac{9}{7}& \text{Uitwerken } \\ & =bx-\frac{9}{7}b+\frac{20}{3}x-\frac{180}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{9}{7}b+\frac{20}{3}x-\frac{60}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-8}{6}-p)(\frac{-5}{4}-p)& =(\color{red}{-p}+\color{orange}{\frac{-4}{3}}).(\color{green}{-p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{4}p+\frac{4}{3}p+\frac{4}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =p^2+(\frac{5}{4}+\frac{4}{3})p+\frac{20}{12} & \text{Neem samen} \\ &=p^2+\frac{31}{12}p+\frac{20}{12} & \text{Maak de som} \\ &=p^2+\frac{31}{12}p+\frac{5}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{7}{18}-a)(x+\frac{-9}{13})& =(\color{red}{-a}+\color{orange}{\frac{7}{18}}).(\color{green}{x}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{7}{18})} . \color{green}{(x)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{13}a+\frac{7}{18}x-\frac{7}{18}.\frac{9}{13}& \text{Uitwerken } \\ & =-ax+\frac{9}{13}a+\frac{7}{18}x-\frac{63}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{9}{13}a+\frac{7}{18}x-\frac{7}{26} & \text{Vereenvoudig} \\\end{align}\)
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