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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-1}{11})(q-\frac{-14}{9})& =(\color{red}{a}+\color{orange}{\frac{1}{11}}).(\color{green}{q}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{1}{11})} . \color{green}{(q)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{14}{9}a+\frac{1}{11}q+\frac{1}{11}.\frac{14}{9}& \text{Uitwerken } \\ & =aq+\frac{14}{9}a+\frac{1}{11}q+\frac{14}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{13}{17})(x+\frac{4}{18})& =(\color{red}{a}+\color{orange}{\frac{13}{17}}).(\color{green}{x}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{13}{17})} . \color{green}{(x)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{9}a+\frac{13}{17}x+\frac{13}{17}.\frac{2}{9}& \text{Uitwerken } \\ & =ax+\frac{2}{9}a+\frac{13}{17}x+\frac{26}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{9}{16})(\frac{1}{3}-x)& =(\color{red}{b}+\color{orange}{\frac{9}{16}}).(\color{green}{-x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{9}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{3}b-\frac{9}{16}x+\frac{9}{16}.\frac{1}{3}& \text{Uitwerken } \\ & =-bx+\frac{1}{3}b-\frac{9}{16}x+\frac{9}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{1}{3}b-\frac{9}{16}x+\frac{3}{16} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{5}{4})(b-\frac{-17}{20})& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{20}a-\frac{5}{4}b-\frac{5}{4}.\frac{17}{20}& \text{Uitwerken } \\ & =ab+\frac{17}{20}a-\frac{5}{4}b-\frac{85}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{17}{20}a-\frac{5}{4}b-\frac{17}{16} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{3}{15}-q)(\frac{13}{4}-q)& =(\color{red}{-q}+\color{orange}{\frac{1}{5}}).(\color{green}{-q}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{13}{4}q-\frac{1}{5}q+\frac{1}{5}.\frac{13}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-13}{4})+(\frac{-1}{5}))q+\frac{13}{20} & \text{Neem samen} \\ &=q^2-\frac{69}{20}q+\frac{13}{20} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-15}{7}+a)(a-\frac{1}{12})& =(\color{red}{a}+\color{orange}{\frac{-15}{7}}).(\color{green}{a}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{12}a-\frac{15}{7}a+\frac{15}{7}.\frac{1}{12}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{12})+(\frac{-15}{7}))a+\frac{15}{84} & \text{Neem samen} \\ &=a^2-\frac{187}{84}a+\frac{15}{84} & \text{Maak de som} \\ &=a^2-\frac{187}{84}a+\frac{5}{28} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(b-\frac{12}{20})(q+\frac{-11}{18})& =(\color{red}{b}+\color{orange}{\frac{-3}{5}}).(\color{green}{q}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{18}b-\frac{3}{5}q+\frac{3}{5}.\frac{11}{18}& \text{Uitwerken } \\ & =bq-\frac{11}{18}b-\frac{3}{5}q+\frac{33}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{11}{18}b-\frac{3}{5}q+\frac{11}{30} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-16}{20})(\frac{14}{5}-q)& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{-q}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{14}{5}x-\frac{4}{5}q+\frac{4}{5}.\frac{14}{5}& \text{Uitwerken } \\ & =-qx+\frac{14}{5}x-\frac{4}{5}q+\frac{56}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{19}{11}-p)(\frac{14}{13}+q)& =(\color{red}{-p}+\color{orange}{\frac{19}{11}}).(\color{green}{q}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(\frac{19}{11})} . \color{green}{(q)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{14}{13}p+\frac{19}{11}q+\frac{19}{11}.\frac{14}{13}& \text{Uitwerken } \\ & =-pq-\frac{14}{13}p+\frac{19}{11}q+\frac{266}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{20}{12}+x)(x-\frac{-3}{15})& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{5}x+\frac{5}{3}x+\frac{5}{3}.\frac{1}{5}& \text{Uitwerken } \\ & =x^2+(\frac{1}{5}+\frac{5}{3})x+\frac{5}{15} & \text{Neem samen} \\ &=x^2+\frac{28}{15}x+\frac{5}{15} & \text{Maak de som} \\ &=x^2+\frac{28}{15}x+\frac{1}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(p+\frac{3}{6})(p-\frac{20}{12})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{3}p+\frac{1}{2}p-\frac{1}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{3})+\frac{1}{2})p-(\frac{-5}{6}) & \text{Neem samen} \\ &=p^2-\frac{7}{6}p-(\frac{-5}{6}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-9}{4}-a)(\frac{4}{17}-x)& =(\color{red}{-a}+\color{orange}{\frac{-9}{4}}).(\color{green}{-x}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{17}a+\frac{9}{4}x-\frac{9}{4}.\frac{4}{17}& \text{Uitwerken } \\ & =ax-\frac{4}{17}a+\frac{9}{4}x-\frac{36}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{4}{17}a+\frac{9}{4}x-\frac{9}{17} & \text{Vereenvoudig} \\\end{align}\)
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