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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-10}{15})(a+\frac{20}{4})& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = aq+5q-\frac{2}{3}a-\frac{2}{3}.5& \text{Uitwerken } \\ & =aq+5q-\frac{2}{3}a-\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-9}{7}-b)(\frac{17}{17}+b)& =(\color{red}{-b}+\color{orange}{\frac{-9}{7}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{-9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bb-1b-\frac{9}{7}b-\frac{9}{7}.1& \text{Uitwerken } \\ & =-b^2+((-1)+(\frac{-9}{7}))b-\frac{9}{7} & \text{Neem samen} \\ &=-b^2-\frac{16}{7}b-\frac{9}{7} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-20}{6})(x+\frac{-5}{12})& =(\color{red}{q}+\color{orange}{\frac{-10}{3}}).(\color{green}{x}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{12}q-\frac{10}{3}x+\frac{10}{3}.\frac{5}{12}& \text{Uitwerken } \\ & =qx-\frac{5}{12}q-\frac{10}{3}x+\frac{50}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{12}q-\frac{10}{3}x+\frac{25}{18} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-17}{10})(\frac{-19}{11}-p)& =(\color{red}{p}+\color{orange}{\frac{17}{10}}).(\color{green}{-p}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{17}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{19}{11}p-\frac{17}{10}p-\frac{17}{10}.\frac{19}{11}& \text{Uitwerken } \\ & =-p^2+((\frac{-19}{11})+(\frac{-17}{10}))p-\frac{323}{110} & \text{Neem samen} \\ &=-p^2-\frac{377}{110}p-\frac{323}{110} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a+\frac{19}{15})(q+\frac{-17}{10})& =(\color{red}{a}+\color{orange}{\frac{19}{15}}).(\color{green}{q}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{19}{15})} . \color{green}{(q)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{10}a+\frac{19}{15}q-\frac{19}{15}.\frac{17}{10}& \text{Uitwerken } \\ & =aq-\frac{17}{10}a+\frac{19}{15}q-\frac{323}{150} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{13}{8})(\frac{18}{13}+b)& =(\color{red}{x}+\color{orange}{\frac{13}{8}}).(\color{green}{b}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{13}{8})} . \color{green}{(b)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{18}{13}x+\frac{13}{8}b+\frac{13}{8}.\frac{18}{13}& \text{Uitwerken } \\ & =bx+\frac{18}{13}x+\frac{13}{8}b+\frac{234}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{18}{13}x+\frac{13}{8}b+\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{5}{18}+x)(x-\frac{19}{12})& =(\color{red}{x}+\color{orange}{\frac{5}{18}}).(\color{green}{x}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{5}{18})} . \color{green}{(x)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{19}{12}x+\frac{5}{18}x-\frac{5}{18}.\frac{19}{12}& \text{Uitwerken } \\ & =x^2+((\frac{-19}{12})+\frac{5}{18})x-(\frac{-95}{216}) & \text{Neem samen} \\ &=x^2-\frac{47}{36}x-(\frac{-95}{216}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-14}{5}+x)(x-\frac{18}{16})& =(\color{red}{x}+\color{orange}{\frac{-14}{5}}).(\color{green}{x}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{9}{8}x-\frac{14}{5}x+\frac{14}{5}.\frac{9}{8}& \text{Uitwerken } \\ & =x^2+((\frac{-9}{8})+(\frac{-14}{5}))x+\frac{126}{40} & \text{Neem samen} \\ &=x^2-\frac{157}{40}x+\frac{126}{40} & \text{Maak de som} \\ &=x^2-\frac{157}{40}x+\frac{63}{20} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{3}{12}+b)(\frac{-5}{7}-q)& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{-q}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{7}b-\frac{1}{4}q-\frac{1}{4}.\frac{5}{7}& \text{Uitwerken } \\ & =-bq-\frac{5}{7}b-\frac{1}{4}q-\frac{5}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{4}{14})(x-\frac{-13}{2})& =(\color{red}{p}+\color{orange}{\frac{-2}{7}}).(\color{green}{x}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{2}p-\frac{2}{7}x-\frac{2}{7}.\frac{13}{2}& \text{Uitwerken } \\ & =px+\frac{13}{2}p-\frac{2}{7}x-\frac{26}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{13}{2}p-\frac{2}{7}x-\frac{13}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{20}{16})(\frac{14}{2}+a)& =(\color{red}{x}+\color{orange}{\frac{5}{4}}).(\color{green}{a}+\color{blue}{7})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(7)} + \color{orange}{(\frac{5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = ax+7x+\frac{5}{4}a+\frac{5}{4}.7& \text{Uitwerken } \\ & =ax+7x+\frac{5}{4}a+\frac{35}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{12}{4}+p)(\frac{12}{8}+b)& =(\color{red}{p}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{2}p+3b+3.\frac{3}{2}& \text{Uitwerken } \\ & =bp+\frac{3}{2}p+3b+\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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