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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-20}{12})(\frac{-9}{13}-a)& =(\color{red}{q}+\color{orange}{\frac{-5}{3}}).(\color{green}{-a}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{9}{13}q+\frac{5}{3}a+\frac{5}{3}.\frac{9}{13}& \text{Uitwerken } \\ & =-aq-\frac{9}{13}q+\frac{5}{3}a+\frac{45}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{9}{13}q+\frac{5}{3}a+\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{4}{8}+p)(x-\frac{8}{8})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1p+\frac{1}{2}x-\frac{1}{2}.1& \text{Uitwerken } \\ & =px-1p+\frac{1}{2}x-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-3}{17})(\frac{10}{8}-q)& =(\color{red}{x}+\color{orange}{\frac{3}{17}}).(\color{green}{-q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{3}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{4}x-\frac{3}{17}q+\frac{3}{17}.\frac{5}{4}& \text{Uitwerken } \\ & =-qx+\frac{5}{4}x-\frac{3}{17}q+\frac{15}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-10}{8}+q)(\frac{-19}{9}-p)& =(\color{red}{q}+\color{orange}{\frac{-5}{4}}).(\color{green}{-p}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{9}q+\frac{5}{4}p+\frac{5}{4}.\frac{19}{9}& \text{Uitwerken } \\ & =-pq-\frac{19}{9}q+\frac{5}{4}p+\frac{95}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{20}{11})(x+\frac{-18}{9})& =(\color{red}{p}+\color{orange}{\frac{-20}{11}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-20}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = px-2p-\frac{20}{11}x+\frac{20}{11}.2& \text{Uitwerken } \\ & =px-2p-\frac{20}{11}x+\frac{40}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{10}{18})(\frac{-15}{3}+b)& =(\color{red}{q}+\color{orange}{\frac{-5}{9}}).(\color{green}{b}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-5)} + \color{orange}{(\frac{-5}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = bq-5q-\frac{5}{9}b+\frac{5}{9}.5& \text{Uitwerken } \\ & =bq-5q-\frac{5}{9}b+\frac{25}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-11}{6})(q+\frac{-13}{7})& =(\color{red}{p}+\color{orange}{\frac{11}{6}}).(\color{green}{q}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{11}{6})} . \color{green}{(q)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{7}p+\frac{11}{6}q-\frac{11}{6}.\frac{13}{7}& \text{Uitwerken } \\ & =pq-\frac{13}{7}p+\frac{11}{6}q-\frac{143}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-19}{18})(q-\frac{1}{4})& =(\color{red}{q}+\color{orange}{\frac{-19}{18}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{4}q-\frac{19}{18}q+\frac{19}{18}.\frac{1}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{4})+(\frac{-19}{18}))q+\frac{19}{72} & \text{Neem samen} \\ &=q^2-\frac{47}{36}q+\frac{19}{72} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-4}{5})(q+\frac{7}{17})& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{q}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{17}x+\frac{4}{5}q+\frac{4}{5}.\frac{7}{17}& \text{Uitwerken } \\ & =qx+\frac{7}{17}x+\frac{4}{5}q+\frac{28}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{20}{3}+p)(\frac{-12}{12}-q)& =(\color{red}{p}+\color{orange}{\frac{20}{3}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{20}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pq-1p-\frac{20}{3}q-\frac{20}{3}.1& \text{Uitwerken } \\ & =-pq-1p-\frac{20}{3}q-\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{11}{15})(x-(-18))& =(\color{red}{x}+\color{orange}{\frac{11}{15}}).(\color{green}{x}+\color{blue}{18})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(18)} + \color{orange}{(\frac{11}{15})} . \color{green}{(x)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = xx+18x+\frac{11}{15}x+\frac{11}{15}.18& \text{Uitwerken } \\ & =x^2+(18+\frac{11}{15})x+\frac{198}{15} & \text{Neem samen} \\ &=x^2+\frac{281}{15}x+\frac{198}{15} & \text{Maak de som} \\ &=x^2+\frac{281}{15}x+\frac{66}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{-12}{8}-b)(q+\frac{2}{20})& =(\color{red}{-b}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{10}b-\frac{3}{2}q-\frac{3}{2}.\frac{1}{10}& \text{Uitwerken } \\ & =-bq-\frac{1}{10}b-\frac{3}{2}q-\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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