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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-8}{11})(\frac{17}{20}+x)& =(\color{red}{a}+\color{orange}{\frac{8}{11}}).(\color{green}{x}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{8}{11})} . \color{green}{(x)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{20}a+\frac{8}{11}x+\frac{8}{11}.\frac{17}{20}& \text{Uitwerken } \\ & =ax+\frac{17}{20}a+\frac{8}{11}x+\frac{136}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{17}{20}a+\frac{8}{11}x+\frac{34}{55} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{3}{14}+a)(\frac{4}{18}-p)& =(\color{red}{a}+\color{orange}{\frac{3}{14}}).(\color{green}{-p}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{3}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{9}a-\frac{3}{14}p+\frac{3}{14}.\frac{2}{9}& \text{Uitwerken } \\ & =-ap+\frac{2}{9}a-\frac{3}{14}p+\frac{6}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{2}{9}a-\frac{3}{14}p+\frac{1}{21} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-9}{18})(\frac{20}{7}-p)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{-p}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{20}{7}a-\frac{1}{2}p+\frac{1}{2}.\frac{20}{7}& \text{Uitwerken } \\ & =-ap+\frac{20}{7}a-\frac{1}{2}p+\frac{20}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{20}{7}a-\frac{1}{2}p+\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{20}+a)(\frac{8}{19}+q)& =(\color{red}{a}+\color{orange}{\frac{9}{20}}).(\color{green}{q}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{9}{20})} . \color{green}{(q)} + \color{orange}{(\frac{9}{20})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{19}a+\frac{9}{20}q+\frac{9}{20}.\frac{8}{19}& \text{Uitwerken } \\ & =aq+\frac{8}{19}a+\frac{9}{20}q+\frac{72}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{8}{19}a+\frac{9}{20}q+\frac{18}{95} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{3}{13})(x+\frac{-15}{10})& =(\color{red}{a}+\color{orange}{\frac{3}{13}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{3}{13})} . \color{green}{(x)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{2}a+\frac{3}{13}x-\frac{3}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =ax-\frac{3}{2}a+\frac{3}{13}x-\frac{9}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-13}{7})(\frac{17}{8}+b)& =(\color{red}{x}+\color{orange}{\frac{13}{7}}).(\color{green}{b}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{13}{7})} . \color{green}{(b)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{8}x+\frac{13}{7}b+\frac{13}{7}.\frac{17}{8}& \text{Uitwerken } \\ & =bx+\frac{17}{8}x+\frac{13}{7}b+\frac{221}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{10}{15})(p-\frac{-1}{6})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{6}q+\frac{2}{3}p+\frac{2}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =pq+\frac{1}{6}q+\frac{2}{3}p+\frac{2}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{6}q+\frac{2}{3}p+\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-17}{10}+p)(\frac{13}{11}-x)& =(\color{red}{p}+\color{orange}{\frac{-17}{10}}).(\color{green}{-x}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{13}{11}p+\frac{17}{10}x-\frac{17}{10}.\frac{13}{11}& \text{Uitwerken } \\ & =-px+\frac{13}{11}p+\frac{17}{10}x-\frac{221}{110} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-10}{16}-p)(\frac{-12}{18}-p)& =(\color{red}{-p}+\color{orange}{\frac{-5}{8}}).(\color{green}{-p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{2}{3}p+\frac{5}{8}p+\frac{5}{8}.\frac{2}{3}& \text{Uitwerken } \\ & =p^2+(\frac{2}{3}+\frac{5}{8})p+\frac{10}{24} & \text{Neem samen} \\ &=p^2+\frac{31}{24}p+\frac{10}{24} & \text{Maak de som} \\ &=p^2+\frac{31}{24}p+\frac{5}{12} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-10}{19}+x)(\frac{9}{14}+x)& =(\color{red}{x}+\color{orange}{\frac{-10}{19}}).(\color{green}{x}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{9}{14}x-\frac{10}{19}x-\frac{10}{19}.\frac{9}{14}& \text{Uitwerken } \\ & =x^2+(\frac{9}{14}+(\frac{-10}{19}))x-(\frac{-90}{266}) & \text{Neem samen} \\ &=x^2+\frac{31}{266}x-(\frac{-90}{266}) & \text{Maak de som} \\ &=x^2+\frac{31}{266}x+\frac{45}{133} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(b-\frac{15}{11})(a-\frac{-16}{18})& =(\color{red}{b}+\color{orange}{\frac{-15}{11}}).(\color{green}{a}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{9}b-\frac{15}{11}a-\frac{15}{11}.\frac{8}{9}& \text{Uitwerken } \\ & =ab+\frac{8}{9}b-\frac{15}{11}a-\frac{120}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{8}{9}b-\frac{15}{11}a-\frac{40}{33} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{7}-b)(\frac{-6}{20}+x)& =(\color{red}{-b}+\color{orange}{\frac{-10}{7}}).(\color{green}{x}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{10}b-\frac{10}{7}x+\frac{10}{7}.\frac{3}{10}& \text{Uitwerken } \\ & =-bx+\frac{3}{10}b-\frac{10}{7}x+\frac{30}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{3}{10}b-\frac{10}{7}x+\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
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