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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{18}{3}-b)(\frac{-5}{7}+q)& =(\color{red}{-b}+\color{orange}{6}).(\color{green}{q}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(6)} . \color{green}{(q)} + \color{orange}{(6)} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{7}b+6q-6.\frac{5}{7}& \text{Uitwerken } \\ & =-bq+\frac{5}{7}b+6q-\frac{30}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{6}{18}+p)(\frac{-11}{20}-p)& =(\color{red}{p}+\color{orange}{\frac{1}{3}}).(\color{green}{-p}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{11}{20}p-\frac{1}{3}p-\frac{1}{3}.\frac{11}{20}& \text{Uitwerken } \\ & =-p^2+((\frac{-11}{20})+(\frac{-1}{3}))p-\frac{11}{60} & \text{Neem samen} \\ &=-p^2-\frac{53}{60}p-\frac{11}{60} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-5}{16}+p)(\frac{-19}{3}+x)& =(\color{red}{p}+\color{orange}{\frac{-5}{16}}).(\color{green}{x}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{-5}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{3}p-\frac{5}{16}x+\frac{5}{16}.\frac{19}{3}& \text{Uitwerken } \\ & =px-\frac{19}{3}p-\frac{5}{16}x+\frac{95}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-1}{14})(\frac{-6}{14}+q)& =(\color{red}{b}+\color{orange}{\frac{-1}{14}}).(\color{green}{q}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{7}b-\frac{1}{14}q+\frac{1}{14}.\frac{3}{7}& \text{Uitwerken } \\ & =bq-\frac{3}{7}b-\frac{1}{14}q+\frac{3}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{19}+p)(\frac{11}{16}-q)& =(\color{red}{p}+\color{orange}{\frac{-16}{19}}).(\color{green}{-q}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{16}p+\frac{16}{19}q-\frac{16}{19}.\frac{11}{16}& \text{Uitwerken } \\ & =-pq+\frac{11}{16}p+\frac{16}{19}q-\frac{176}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{11}{16}p+\frac{16}{19}q-\frac{11}{19} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{8}{17}-a)(\frac{11}{4}+q)& =(\color{red}{-a}+\color{orange}{\frac{8}{17}}).(\color{green}{q}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{8}{17})} . \color{green}{(q)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{11}{4}a+\frac{8}{17}q+\frac{8}{17}.\frac{11}{4}& \text{Uitwerken } \\ & =-aq-\frac{11}{4}a+\frac{8}{17}q+\frac{88}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{11}{4}a+\frac{8}{17}q+\frac{22}{17} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{4}+p)(\frac{-4}{15}+a)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{4}{15}p+2a-2.\frac{4}{15}& \text{Uitwerken } \\ & =ap-\frac{4}{15}p+2a-\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-13}{11})(\frac{13}{10}-a)& =(\color{red}{a}+\color{orange}{\frac{13}{11}}).(\color{green}{-a}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{13}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{13}{10}a-\frac{13}{11}a+\frac{13}{11}.\frac{13}{10}& \text{Uitwerken } \\ & =-a^2+(\frac{13}{10}+(\frac{-13}{11}))a+(\frac{-169}{110}) & \text{Neem samen} \\ &=-a^2+\frac{13}{110}a+(\frac{-169}{110}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{17}{20}+a)(\frac{-16}{13}-q)& =(\color{red}{a}+\color{orange}{\frac{17}{20}}).(\color{green}{-q}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{17}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{16}{13}a-\frac{17}{20}q-\frac{17}{20}.\frac{16}{13}& \text{Uitwerken } \\ & =-aq-\frac{16}{13}a-\frac{17}{20}q-\frac{272}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{16}{13}a-\frac{17}{20}q-\frac{68}{65} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{11}{5})(x+\frac{3}{4})& =(\color{red}{b}+\color{orange}{\frac{-11}{5}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{4}b-\frac{11}{5}x-\frac{11}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =bx+\frac{3}{4}b-\frac{11}{5}x-\frac{33}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-15}{7})(\frac{-19}{5}+q)& =(\color{red}{p}+\color{orange}{\frac{15}{7}}).(\color{green}{q}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{15}{7})} . \color{green}{(q)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{5}p+\frac{15}{7}q-\frac{15}{7}.\frac{19}{5}& \text{Uitwerken } \\ & =pq-\frac{19}{5}p+\frac{15}{7}q-\frac{285}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{19}{5}p+\frac{15}{7}q-\frac{57}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{11}+b)(\frac{14}{14}-x)& =(\color{red}{b}+\color{orange}{\frac{13}{11}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{13}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1b-\frac{13}{11}x+\frac{13}{11}.1& \text{Uitwerken } \\ & =-bx+1b-\frac{13}{11}x+\frac{13}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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