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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-2}{6})(q+\frac{4}{18})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{9}x+\frac{1}{3}q+\frac{1}{3}.\frac{2}{9}& \text{Uitwerken } \\ & =qx+\frac{2}{9}x+\frac{1}{3}q+\frac{2}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-1}{9})(a-(-17))& =(\color{red}{q}+\color{orange}{\frac{-1}{9}}).(\color{green}{a}+\color{blue}{17})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(17)} + \color{orange}{(\frac{-1}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = aq+17q-\frac{1}{9}a-\frac{1}{9}.17& \text{Uitwerken } \\ & =aq+17q-\frac{1}{9}a-\frac{17}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-5)(b+\frac{-10}{6})& =(\color{red}{p}+\color{orange}{(-5)}).(\color{green}{b}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(-5)} . \color{green}{(b)} + \color{orange}{(-5)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{3}p-5b+5.\frac{5}{3}& \text{Uitwerken } \\ & =bp-\frac{5}{3}p-5b+\frac{25}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{11}{16})(\frac{12}{3}-x)& =(\color{red}{q}+\color{orange}{\frac{-11}{16}}).(\color{green}{-x}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(4)} + \color{orange}{(\frac{-11}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -qx+4q+\frac{11}{16}x-\frac{11}{16}.4& \text{Uitwerken } \\ & =-qx+4q+\frac{11}{16}x-\frac{44}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+4q+\frac{11}{16}x-\frac{11}{4} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b-\frac{3}{13})(\frac{-7}{17}+q)& =(\color{red}{b}+\color{orange}{\frac{-3}{13}}).(\color{green}{q}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{17}b-\frac{3}{13}q+\frac{3}{13}.\frac{7}{17}& \text{Uitwerken } \\ & =bq-\frac{7}{17}b-\frac{3}{13}q+\frac{21}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{17}{6}+q)(a+\frac{-20}{19})& =(\color{red}{q}+\color{orange}{\frac{17}{6}}).(\color{green}{a}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{17}{6})} . \color{green}{(a)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{20}{19}q+\frac{17}{6}a-\frac{17}{6}.\frac{20}{19}& \text{Uitwerken } \\ & =aq-\frac{20}{19}q+\frac{17}{6}a-\frac{340}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{20}{19}q+\frac{17}{6}a-\frac{170}{57} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-16}{9}+p)(\frac{20}{9}+x)& =(\color{red}{p}+\color{orange}{\frac{-16}{9}}).(\color{green}{x}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{20}{9}p-\frac{16}{9}x-\frac{16}{9}.\frac{20}{9}& \text{Uitwerken } \\ & =px+\frac{20}{9}p-\frac{16}{9}x-\frac{320}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-13}{9}+b)(\frac{18}{12}+q)& =(\color{red}{b}+\color{orange}{\frac{-13}{9}}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{2}b-\frac{13}{9}q-\frac{13}{9}.\frac{3}{2}& \text{Uitwerken } \\ & =bq+\frac{3}{2}b-\frac{13}{9}q-\frac{39}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{3}{2}b-\frac{13}{9}q-\frac{13}{6} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{19}{4}-a)(p-\frac{11}{9})& =(\color{red}{-a}+\color{orange}{\frac{19}{4}}).(\color{green}{p}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(\frac{19}{4})} . \color{green}{(p)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{11}{9}a+\frac{19}{4}p-\frac{19}{4}.\frac{11}{9}& \text{Uitwerken } \\ & =-ap+\frac{11}{9}a+\frac{19}{4}p-\frac{209}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-20}{12})(\frac{6}{13}+b)& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{b}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{6}{13}b-\frac{5}{3}b-\frac{5}{3}.\frac{6}{13}& \text{Uitwerken } \\ & =b^2+(\frac{6}{13}+(\frac{-5}{3}))b-(\frac{-30}{39}) & \text{Neem samen} \\ &=b^2-\frac{47}{39}b-(\frac{-30}{39}) & \text{Maak de som} \\ &=b^2-\frac{47}{39}b+\frac{10}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-8}{3})(\frac{6}{12}+p)& =(\color{red}{p}+\color{orange}{\frac{-8}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{2}p-\frac{8}{3}p-\frac{8}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =p^2+(\frac{1}{2}+(\frac{-8}{3}))p-(\frac{-8}{6}) & \text{Neem samen} \\ &=p^2-\frac{13}{6}p-(\frac{-8}{6}) & \text{Maak de som} \\ &=p^2-\frac{13}{6}p+\frac{4}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-17}{13})(\frac{-10}{20}-q)& =(\color{red}{q}+\color{orange}{\frac{17}{13}}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{17}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{2}q-\frac{17}{13}q-\frac{17}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{2})+(\frac{-17}{13}))q-\frac{17}{26} & \text{Neem samen} \\ &=-q^2-\frac{47}{26}q-\frac{17}{26} & \text{Maak de som} \\\end{align}\)
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