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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{3}{9}+q)(p-\frac{-5}{17})& =(\color{red}{q}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{17}q+\frac{1}{3}p+\frac{1}{3}.\frac{5}{17}& \text{Uitwerken } \\ & =pq+\frac{5}{17}q+\frac{1}{3}p+\frac{5}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-14}{7})(\frac{9}{4}+x)& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{4}a-2x-2.\frac{9}{4}& \text{Uitwerken } \\ & =ax+\frac{9}{4}a-2x-\frac{18}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{9}{4}a-2x-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{8}{7})(\frac{-1}{10}+p)& =(\color{red}{b}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{10}b-\frac{8}{7}p+\frac{8}{7}.\frac{1}{10}& \text{Uitwerken } \\ & =bp-\frac{1}{10}b-\frac{8}{7}p+\frac{8}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{1}{10}b-\frac{8}{7}p+\frac{4}{35} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-8}{15}+a)(\frac{-4}{17}+b)& =(\color{red}{a}+\color{orange}{\frac{-8}{15}}).(\color{green}{b}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{17}a-\frac{8}{15}b+\frac{8}{15}.\frac{4}{17}& \text{Uitwerken } \\ & =ab-\frac{4}{17}a-\frac{8}{15}b+\frac{32}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-18}{2})(\frac{7}{12}-a)& =(\color{red}{q}+\color{orange}{9}).(\color{green}{-a}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(9)} . \color{green}{(-a)} + \color{orange}{(9)} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{12}q-9a+9.\frac{7}{12}& \text{Uitwerken } \\ & =-aq+\frac{7}{12}q-9a+\frac{63}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{7}{12}q-9a+\frac{21}{4} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{1}{11}-a)(a-\frac{-13}{12})& =(\color{red}{-a}+\color{orange}{\frac{1}{11}}).(\color{green}{a}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{1}{11})} . \color{green}{(a)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{13}{12}a+\frac{1}{11}a+\frac{1}{11}.\frac{13}{12}& \text{Uitwerken } \\ & =-a^2+((\frac{-13}{12})+\frac{1}{11})a+(\frac{-13}{132}) & \text{Neem samen} \\ &=-a^2-\frac{131}{132}a+(\frac{-13}{132}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{16}-q)(a+\frac{-18}{10})& =(\color{red}{-q}+\color{orange}{\frac{-9}{16}}).(\color{green}{a}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{5}q-\frac{9}{16}a+\frac{9}{16}.\frac{9}{5}& \text{Uitwerken } \\ & =-aq+\frac{9}{5}q-\frac{9}{16}a+\frac{81}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-18}{18}-p)(a+\frac{8}{17})& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{8}{17}p-1a-1.\frac{8}{17}& \text{Uitwerken } \\ & =-ap-\frac{8}{17}p-1a-\frac{8}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-6}{5})((-20)+b)& =(\color{red}{a}+\color{orange}{\frac{-6}{5}}).(\color{green}{b}+\color{blue}{(-20)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-20)} + \color{orange}{(\frac{-6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = ab-20a-\frac{6}{5}b+\frac{6}{5}.20& \text{Uitwerken } \\ & =ab-20a-\frac{6}{5}b+\frac{120}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-20a-\frac{6}{5}b+24 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-8}{6})(x-(-6))& =(\color{red}{a}+\color{orange}{\frac{-4}{3}}).(\color{green}{x}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(6)} + \color{orange}{(\frac{-4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = ax+6a-\frac{4}{3}x-\frac{4}{3}.6& \text{Uitwerken } \\ & =ax+6a-\frac{4}{3}x-\frac{24}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+6a-\frac{4}{3}x-8 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a+\frac{13}{11})(\frac{-15}{14}-p)& =(\color{red}{a}+\color{orange}{\frac{13}{11}}).(\color{green}{-p}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(\frac{13}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{15}{14}a-\frac{13}{11}p-\frac{13}{11}.\frac{15}{14}& \text{Uitwerken } \\ & =-ap-\frac{15}{14}a-\frac{13}{11}p-\frac{195}{154} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{3}{11}+p)(p+\frac{-19}{20})& =(\color{red}{p}+\color{orange}{\frac{3}{11}}).(\color{green}{p}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{3}{11})} . \color{green}{(p)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{19}{20}p+\frac{3}{11}p-\frac{3}{11}.\frac{19}{20}& \text{Uitwerken } \\ & =p^2+((\frac{-19}{20})+\frac{3}{11})p-(\frac{-57}{220}) & \text{Neem samen} \\ &=p^2-\frac{149}{220}p-(\frac{-57}{220}) & \text{Maak de som} \\\end{align}\)
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