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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{2}{11})(a+\frac{-16}{2})& =(\color{red}{a}+\color{orange}{\frac{-2}{11}}).(\color{green}{a}+\color{blue}{(-8)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-8)} + \color{orange}{(\frac{-2}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = aa-8a-\frac{2}{11}a+\frac{2}{11}.8& \text{Uitwerken } \\ & =a^2+((-8)+(\frac{-2}{11}))a+\frac{16}{11} & \text{Neem samen} \\ &=a^2-\frac{90}{11}a+\frac{16}{11} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-13}{16}-p)(a-\frac{-16}{15})& =(\color{red}{-p}+\color{orange}{\frac{-13}{16}}).(\color{green}{a}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{16}{15}p-\frac{13}{16}a-\frac{13}{16}.\frac{16}{15}& \text{Uitwerken } \\ & =-ap-\frac{16}{15}p-\frac{13}{16}a-\frac{208}{240} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{16}{15}p-\frac{13}{16}a-\frac{13}{15} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-11}{13})(\frac{18}{9}+a)& =(\color{red}{p}+\color{orange}{\frac{-11}{13}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-11}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2p-\frac{11}{13}a-\frac{11}{13}.2& \text{Uitwerken } \\ & =ap+2p-\frac{11}{13}a-\frac{22}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(4-a)(\frac{6}{19}+a)& =(\color{red}{-a}+\color{orange}{4}).(\color{green}{a}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{6}{19}a+4a+4.\frac{6}{19}& \text{Uitwerken } \\ & =-a^2+((\frac{-6}{19})+4)a+(\frac{-24}{19}) & \text{Neem samen} \\ &=-a^2+\frac{70}{19}a+(\frac{-24}{19}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(q+\frac{6}{20})(p+\frac{-10}{19})& =(\color{red}{q}+\color{orange}{\frac{3}{10}}).(\color{green}{p}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{10}{19}q+\frac{3}{10}p-\frac{3}{10}.\frac{10}{19}& \text{Uitwerken } \\ & =pq-\frac{10}{19}q+\frac{3}{10}p-\frac{30}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{10}{19}q+\frac{3}{10}p-\frac{3}{19} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-18}{17})(\frac{15}{19}-q)& =(\color{red}{b}+\color{orange}{\frac{-18}{17}}).(\color{green}{-q}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{15}{19}b+\frac{18}{17}q-\frac{18}{17}.\frac{15}{19}& \text{Uitwerken } \\ & =-bq+\frac{15}{19}b+\frac{18}{17}q-\frac{270}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-14}{10})(\frac{13}{11}+x)& =(\color{red}{a}+\color{orange}{\frac{7}{5}}).(\color{green}{x}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{13}{11}a+\frac{7}{5}x+\frac{7}{5}.\frac{13}{11}& \text{Uitwerken } \\ & =ax+\frac{13}{11}a+\frac{7}{5}x+\frac{91}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{20}{7})(p+\frac{-4}{6})& =(\color{red}{q}+\color{orange}{\frac{20}{7}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{20}{7})} . \color{green}{(p)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{3}q+\frac{20}{7}p-\frac{20}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =pq-\frac{2}{3}q+\frac{20}{7}p-\frac{40}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-9}{14})(\frac{-7}{5}+x)& =(\color{red}{b}+\color{orange}{\frac{9}{14}}).(\color{green}{x}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{9}{14})} . \color{green}{(x)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{5}b+\frac{9}{14}x-\frac{9}{14}.\frac{7}{5}& \text{Uitwerken } \\ & =bx-\frac{7}{5}b+\frac{9}{14}x-\frac{63}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{7}{5}b+\frac{9}{14}x-\frac{9}{10} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-19}{15}+q)(a+\frac{-15}{8})& =(\color{red}{q}+\color{orange}{\frac{-19}{15}}).(\color{green}{a}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{-19}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{8}q-\frac{19}{15}a+\frac{19}{15}.\frac{15}{8}& \text{Uitwerken } \\ & =aq-\frac{15}{8}q-\frac{19}{15}a+\frac{285}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{15}{8}q-\frac{19}{15}a+\frac{19}{8} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{18}{12})(\frac{-11}{19}+b)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{19}x+\frac{3}{2}b-\frac{3}{2}.\frac{11}{19}& \text{Uitwerken } \\ & =bx-\frac{11}{19}x+\frac{3}{2}b-\frac{33}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-10}{20})(\frac{17}{16}+p)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{17}{16}b+\frac{1}{2}p+\frac{1}{2}.\frac{17}{16}& \text{Uitwerken } \\ & =bp+\frac{17}{16}b+\frac{1}{2}p+\frac{17}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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