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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{17}{7})(q-\frac{5}{11})& =(\color{red}{q}+\color{orange}{\frac{17}{7}}).(\color{green}{q}+\color{blue}{\frac{-5}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{11})} + \color{orange}{(\frac{17}{7})} . \color{green}{(q)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{-5}{11})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{5}{11}q+\frac{17}{7}q-\frac{17}{7}.\frac{5}{11}& \text{Uitwerken } \\ & =q^2+((\frac{-5}{11})+\frac{17}{7})q-(\frac{-85}{77}) & \text{Neem samen} \\ &=q^2+\frac{152}{77}q-(\frac{-85}{77}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-8}{18}-x)(q-\frac{11}{2})& =(\color{red}{-x}+\color{orange}{\frac{-4}{9}}).(\color{green}{q}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{11}{2}x-\frac{4}{9}q+\frac{4}{9}.\frac{11}{2}& \text{Uitwerken } \\ & =-qx+\frac{11}{2}x-\frac{4}{9}q+\frac{44}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{11}{2}x-\frac{4}{9}q+\frac{22}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a-\frac{16}{9})(a-\frac{15}{6})& =(\color{red}{a}+\color{orange}{\frac{-16}{9}}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{2}a-\frac{16}{9}a+\frac{16}{9}.\frac{5}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{2})+(\frac{-16}{9}))a+\frac{80}{18} & \text{Neem samen} \\ &=a^2-\frac{77}{18}a+\frac{80}{18} & \text{Maak de som} \\ &=a^2-\frac{77}{18}a+\frac{40}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{8}{6}-x)(\frac{18}{3}+x)& =(\color{red}{-x}+\color{orange}{\frac{4}{3}}).(\color{green}{x}+\color{blue}{6})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(6)} + \color{orange}{(\frac{4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -xx-6x+\frac{4}{3}x+\frac{4}{3}.6& \text{Uitwerken } \\ & =-x^2+((-6)+\frac{4}{3})x+(\frac{-24}{3}) & \text{Neem samen} \\ &=-x^2-\frac{14}{3}x+(\frac{-24}{3}) & \text{Maak de som} \\ &=-x^2-\frac{14}{3}x+(-8) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{15}{14}-p)(\frac{-16}{20}+q)& =(\color{red}{-p}+\color{orange}{\frac{15}{14}}).(\color{green}{q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{15}{14})} . \color{green}{(q)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{4}{5}p+\frac{15}{14}q-\frac{15}{14}.\frac{4}{5}& \text{Uitwerken } \\ & =-pq+\frac{4}{5}p+\frac{15}{14}q-\frac{60}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{4}{5}p+\frac{15}{14}q-\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{6}{13}+x)(p-\frac{19}{7})& =(\color{red}{x}+\color{orange}{\frac{6}{13}}).(\color{green}{p}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{6}{13})} . \color{green}{(p)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{7}x+\frac{6}{13}p-\frac{6}{13}.\frac{19}{7}& \text{Uitwerken } \\ & =px-\frac{19}{7}x+\frac{6}{13}p-\frac{114}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{-18}{19})(\frac{-20}{10}+p)& =(\color{red}{p}+\color{orange}{\frac{-18}{19}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-18}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pp-2p-\frac{18}{19}p+\frac{18}{19}.2& \text{Uitwerken } \\ & =p^2+((-2)+(\frac{-18}{19}))p+\frac{36}{19} & \text{Neem samen} \\ &=p^2-\frac{56}{19}p+\frac{36}{19} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(x+\frac{14}{8})(\frac{15}{17}+b)& =(\color{red}{x}+\color{orange}{\frac{7}{4}}).(\color{green}{b}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{17}x+\frac{7}{4}b+\frac{7}{4}.\frac{15}{17}& \text{Uitwerken } \\ & =bx+\frac{15}{17}x+\frac{7}{4}b+\frac{105}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{18}{2}+x)(b-\frac{-7}{2})& =(\color{red}{x}+\color{orange}{9}).(\color{green}{b}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(9)} . \color{green}{(b)} + \color{orange}{(9)} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{2}x+9b+9.\frac{7}{2}& \text{Uitwerken } \\ & =bx+\frac{7}{2}x+9b+\frac{63}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-4}{20}-b)(q+\frac{9}{6})& =(\color{red}{-b}+\color{orange}{\frac{-1}{5}}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{2}b-\frac{1}{5}q-\frac{1}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =-bq-\frac{3}{2}b-\frac{1}{5}q-\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{5}{12})(\frac{3}{19}+b)& =(\color{red}{x}+\color{orange}{\frac{5}{12}}).(\color{green}{b}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{5}{12})} . \color{green}{(b)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{19}x+\frac{5}{12}b+\frac{5}{12}.\frac{3}{19}& \text{Uitwerken } \\ & =bx+\frac{3}{19}x+\frac{5}{12}b+\frac{15}{228} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{19}x+\frac{5}{12}b+\frac{5}{76} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-19}{2}+a)(x-\frac{8}{6})& =(\color{red}{a}+\color{orange}{\frac{-19}{2}}).(\color{green}{x}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{3}a-\frac{19}{2}x+\frac{19}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =ax-\frac{4}{3}a-\frac{19}{2}x+\frac{76}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{4}{3}a-\frac{19}{2}x+\frac{38}{3} & \text{Vereenvoudig} \\\end{align}\)
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