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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-6}{16})(\frac{9}{11}-x)& =(\color{red}{q}+\color{orange}{\frac{3}{8}}).(\color{green}{-x}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{3}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{9}{11}q-\frac{3}{8}x+\frac{3}{8}.\frac{9}{11}& \text{Uitwerken } \\ & =-qx+\frac{9}{11}q-\frac{3}{8}x+\frac{27}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-8}{20})(\frac{11}{12}-b)& =(\color{red}{p}+\color{orange}{\frac{2}{5}}).(\color{green}{-b}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{11}{12}p-\frac{2}{5}b+\frac{2}{5}.\frac{11}{12}& \text{Uitwerken } \\ & =-bp+\frac{11}{12}p-\frac{2}{5}b+\frac{22}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{11}{12}p-\frac{2}{5}b+\frac{11}{30} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}((-7)+x)(\frac{4}{2}+x)& =(\color{red}{x}+\color{orange}{(-7)}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(-7)} . \color{green}{(x)} + \color{orange}{(-7)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = xx+2x-7x-7.2& \text{Uitwerken } \\ & =x^2+(2+(-7))x-(-14) & \text{Neem samen} \\ &=x^2-5x-(-14) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-1}{4}-a)(\frac{11}{15}-x)& =(\color{red}{-a}+\color{orange}{\frac{-1}{4}}).(\color{green}{-x}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{15}a+\frac{1}{4}x-\frac{1}{4}.\frac{11}{15}& \text{Uitwerken } \\ & =ax-\frac{11}{15}a+\frac{1}{4}x-\frac{11}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-18}{11}+p)(b+12)& =(\color{red}{p}+\color{orange}{\frac{-18}{11}}).(\color{green}{b}+\color{blue}{12})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(12)} + \color{orange}{(\frac{-18}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-18}{11})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = bp+12p-\frac{18}{11}b-\frac{18}{11}.12& \text{Uitwerken } \\ & =bp+12p-\frac{18}{11}b-\frac{216}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-5}{10}-a)(\frac{16}{5}-a)& =(\color{red}{-a}+\color{orange}{\frac{-1}{2}}).(\color{green}{-a}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{16}{5}a+\frac{1}{2}a-\frac{1}{2}.\frac{16}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-16}{5})+\frac{1}{2})a-(\frac{-16}{10}) & \text{Neem samen} \\ &=a^2-\frac{27}{10}a-(\frac{-16}{10}) & \text{Maak de som} \\ &=a^2-\frac{27}{10}a+\frac{8}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(a-\frac{4}{14})(p-\frac{-18}{20})& =(\color{red}{a}+\color{orange}{\frac{-2}{7}}).(\color{green}{p}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{10}a-\frac{2}{7}p-\frac{2}{7}.\frac{9}{10}& \text{Uitwerken } \\ & =ap+\frac{9}{10}a-\frac{2}{7}p-\frac{18}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{9}{10}a-\frac{2}{7}p-\frac{9}{35} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-19}{2})(b+\frac{-6}{3})& =(\color{red}{q}+\color{orange}{\frac{-19}{2}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-19}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bq-2q-\frac{19}{2}b+\frac{19}{2}.2& \text{Uitwerken } \\ & =bq-2q-\frac{19}{2}b+\frac{38}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-2q-\frac{19}{2}b+19 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-14}{7})(b-\frac{-9}{4})& =(\color{red}{b}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{9}{4}b+2b+2.\frac{9}{4}& \text{Uitwerken } \\ & =b^2+(\frac{9}{4}+2)b+\frac{18}{4} & \text{Neem samen} \\ &=b^2+\frac{17}{4}b+\frac{18}{4} & \text{Maak de som} \\ &=b^2+\frac{17}{4}b+\frac{9}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{20}{13}-p)(b-\frac{-14}{15})& =(\color{red}{-p}+\color{orange}{\frac{20}{13}}).(\color{green}{b}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(\frac{20}{13})} . \color{green}{(b)} + \color{orange}{(\frac{20}{13})} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{14}{15}p+\frac{20}{13}b+\frac{20}{13}.\frac{14}{15}& \text{Uitwerken } \\ & =-bp-\frac{14}{15}p+\frac{20}{13}b+\frac{280}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{14}{15}p+\frac{20}{13}b+\frac{56}{39} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{20}{8}-q)(\frac{7}{14}-q)& =(\color{red}{-q}+\color{orange}{\frac{5}{2}}).(\color{green}{-q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{2}q-\frac{5}{2}q+\frac{5}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{2})+(\frac{-5}{2}))q+\frac{5}{4} & \text{Neem samen} \\ &=q^2-\frac{6}{2}q+\frac{5}{4} & \text{Maak de som} \\ &=q^2-3q+\frac{5}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(19+x)(\frac{17}{7}-a)& =(\color{red}{x}+\color{orange}{19}).(\color{green}{-a}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(19)} . \color{green}{(-a)} + \color{orange}{(19)} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{17}{7}x-19a+19.\frac{17}{7}& \text{Uitwerken } \\ & =-ax+\frac{17}{7}x-19a+\frac{323}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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