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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-3}{3}+b)(b-\frac{19}{12})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{19}{12}b-1b+1.\frac{19}{12}& \text{Uitwerken } \\ & =b^2+((\frac{-19}{12})+(-1))b+\frac{19}{12} & \text{Neem samen} \\ &=b^2-\frac{31}{12}b+\frac{19}{12} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{5}{17}+p)(q-\frac{17}{6})& =(\color{red}{p}+\color{orange}{\frac{5}{17}}).(\color{green}{q}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{5}{17})} . \color{green}{(q)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{6}p+\frac{5}{17}q-\frac{5}{17}.\frac{17}{6}& \text{Uitwerken } \\ & =pq-\frac{17}{6}p+\frac{5}{17}q-\frac{85}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{17}{6}p+\frac{5}{17}q-\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-8}{11})(\frac{1}{16}+a)& =(\color{red}{b}+\color{orange}{\frac{8}{11}}).(\color{green}{a}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{8}{11})} . \color{green}{(a)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{16}b+\frac{8}{11}a+\frac{8}{11}.\frac{1}{16}& \text{Uitwerken } \\ & =ab+\frac{1}{16}b+\frac{8}{11}a+\frac{8}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{16}b+\frac{8}{11}a+\frac{1}{22} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b-\frac{2}{3})(q-\frac{4}{2})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bq-2b-\frac{2}{3}q+\frac{2}{3}.2& \text{Uitwerken } \\ & =bq-2b-\frac{2}{3}q+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{19}+a)(\frac{-2}{10}+b)& =(\color{red}{a}+\color{orange}{\frac{-16}{19}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{5}a-\frac{16}{19}b+\frac{16}{19}.\frac{1}{5}& \text{Uitwerken } \\ & =ab-\frac{1}{5}a-\frac{16}{19}b+\frac{16}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{12}{12})(\frac{18}{12}+b)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{2}x-1b-1.\frac{3}{2}& \text{Uitwerken } \\ & =bx+\frac{3}{2}x-1b-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{17}{9})(q+\frac{-17}{16})& =(\color{red}{x}+\color{orange}{\frac{17}{9}}).(\color{green}{q}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{17}{9})} . \color{green}{(q)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{16}x+\frac{17}{9}q-\frac{17}{9}.\frac{17}{16}& \text{Uitwerken } \\ & =qx-\frac{17}{16}x+\frac{17}{9}q-\frac{289}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{19}{15}+x)(\frac{-3}{10}-x)& =(\color{red}{x}+\color{orange}{\frac{19}{15}}).(\color{green}{-x}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{19}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{3}{10}x-\frac{19}{15}x-\frac{19}{15}.\frac{3}{10}& \text{Uitwerken } \\ & =-x^2+((\frac{-3}{10})+(\frac{-19}{15}))x-\frac{57}{150} & \text{Neem samen} \\ &=-x^2-\frac{47}{30}x-\frac{57}{150} & \text{Maak de som} \\ &=-x^2-\frac{47}{30}x-\frac{19}{50} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-8}{9}-b)(\frac{-10}{15}+b)& =(\color{red}{-b}+\color{orange}{\frac{-8}{9}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{2}{3}b-\frac{8}{9}b+\frac{8}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =-b^2+(\frac{2}{3}+(\frac{-8}{9}))b+(\frac{-16}{27}) & \text{Neem samen} \\ &=-b^2-\frac{2}{9}b+(\frac{-16}{27}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{10}{6}+q)(\frac{18}{5}+b)& =(\color{red}{q}+\color{orange}{\frac{5}{3}}).(\color{green}{b}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{5}q+\frac{5}{3}b+\frac{5}{3}.\frac{18}{5}& \text{Uitwerken } \\ & =bq+\frac{18}{5}q+\frac{5}{3}b+\frac{90}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{18}{5}q+\frac{5}{3}b+6 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q-\frac{9}{16})(q+\frac{3}{6})& =(\color{red}{q}+\color{orange}{\frac{-9}{16}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{2}q-\frac{9}{16}q-\frac{9}{16}.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+(\frac{1}{2}+(\frac{-9}{16}))q-(\frac{-9}{32}) & \text{Neem samen} \\ &=q^2-\frac{1}{16}q-(\frac{-9}{32}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-13}{10})(b-\frac{13}{14})& =(\color{red}{q}+\color{orange}{\frac{-13}{10}}).(\color{green}{b}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{14}q-\frac{13}{10}b+\frac{13}{10}.\frac{13}{14}& \text{Uitwerken } \\ & =bq-\frac{13}{14}q-\frac{13}{10}b+\frac{169}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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