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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{13}-q)(q+\frac{-6}{4})& =(\color{red}{-q}+\color{orange}{\frac{-19}{13}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{3}{2}q-\frac{19}{13}q+\frac{19}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =-q^2+(\frac{3}{2}+(\frac{-19}{13}))q+(\frac{-57}{26}) & \text{Neem samen} \\ &=-q^2+\frac{1}{26}q+(\frac{-57}{26}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{18}+p)(x+\frac{5}{20})& =(\color{red}{p}+\color{orange}{\frac{4}{9}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{4}{9})} . \color{green}{(x)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{4}p+\frac{4}{9}x+\frac{4}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =px+\frac{1}{4}p+\frac{4}{9}x+\frac{4}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{4}p+\frac{4}{9}x+\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{1}{7}-q)(\frac{-13}{10}+x)& =(\color{red}{-q}+\color{orange}{\frac{1}{7}}).(\color{green}{x}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{1}{7})} . \color{green}{(x)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{10}q+\frac{1}{7}x-\frac{1}{7}.\frac{13}{10}& \text{Uitwerken } \\ & =-qx+\frac{13}{10}q+\frac{1}{7}x-\frac{13}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-8}{9}+p)(a-\frac{-16}{6})& =(\color{red}{p}+\color{orange}{\frac{-8}{9}}).(\color{green}{a}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{3}p-\frac{8}{9}a-\frac{8}{9}.\frac{8}{3}& \text{Uitwerken } \\ & =ap+\frac{8}{3}p-\frac{8}{9}a-\frac{64}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-14}{9}-a)(\frac{3}{20}-a)& =(\color{red}{-a}+\color{orange}{\frac{-14}{9}}).(\color{green}{-a}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{20}a+\frac{14}{9}a-\frac{14}{9}.\frac{3}{20}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{20})+\frac{14}{9})a-(\frac{-42}{180}) & \text{Neem samen} \\ &=a^2+\frac{253}{180}a-(\frac{-42}{180}) & \text{Maak de som} \\ &=a^2+\frac{253}{180}a+\frac{7}{30} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(\frac{-4}{12}-x)(b-\frac{-19}{2})& =(\color{red}{-x}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{19}{2}x-\frac{1}{3}b-\frac{1}{3}.\frac{19}{2}& \text{Uitwerken } \\ & =-bx-\frac{19}{2}x-\frac{1}{3}b-\frac{19}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{9}{7})(p-\frac{-14}{7})& =(\color{red}{q}+\color{orange}{\frac{9}{7}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{9}{7})} . \color{green}{(p)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2q+\frac{9}{7}p+\frac{9}{7}.2& \text{Uitwerken } \\ & =pq+2q+\frac{9}{7}p+\frac{18}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-8}{9})(\frac{3}{19}-x)& =(\color{red}{a}+\color{orange}{\frac{8}{9}}).(\color{green}{-x}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{8}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{19}a-\frac{8}{9}x+\frac{8}{9}.\frac{3}{19}& \text{Uitwerken } \\ & =-ax+\frac{3}{19}a-\frac{8}{9}x+\frac{24}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{3}{19}a-\frac{8}{9}x+\frac{8}{57} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-8}{3})(3+q)& =(\color{red}{b}+\color{orange}{\frac{8}{3}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(\frac{8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bq+3b+\frac{8}{3}q+\frac{8}{3}.3& \text{Uitwerken } \\ & =bq+3b+\frac{8}{3}q+\frac{24}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+3b+\frac{8}{3}q+8 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{12}{4})(p-\frac{-4}{2})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bp+2b-3p-3.2& \text{Uitwerken } \\ & =bp+2b-3p-6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{19}{16}-q)(\frac{-11}{16}-q)& =(\color{red}{-q}+\color{orange}{\frac{19}{16}}).(\color{green}{-q}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(\frac{19}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{11}{16}q-\frac{19}{16}q-\frac{19}{16}.\frac{11}{16}& \text{Uitwerken } \\ & =q^2+(\frac{11}{16}+(\frac{-19}{16}))q-(\frac{-209}{256}) & \text{Neem samen} \\ &=q^2-\frac{8}{16}q-(\frac{-209}{256}) & \text{Maak de som} \\ &=q^2-\frac{1}{2}q+\frac{209}{256} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-2}{7})(a+\frac{-17}{16})& =(\color{red}{x}+\color{orange}{\frac{-2}{7}}).(\color{green}{a}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{16}x-\frac{2}{7}a+\frac{2}{7}.\frac{17}{16}& \text{Uitwerken } \\ & =ax-\frac{17}{16}x-\frac{2}{7}a+\frac{34}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{17}{16}x-\frac{2}{7}a+\frac{17}{56} & \text{Vereenvoudig} \\\end{align}\)
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