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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{5}{11}-b)(b-\frac{-4}{15})& =(\color{red}{-b}+\color{orange}{\frac{5}{11}}).(\color{green}{b}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{5}{11})} . \color{green}{(b)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{4}{15}b+\frac{5}{11}b+\frac{5}{11}.\frac{4}{15}& \text{Uitwerken } \\ & =-b^2+((\frac{-4}{15})+\frac{5}{11})b+(\frac{-20}{165}) & \text{Neem samen} \\ &=-b^2+\frac{31}{165}b+(\frac{-20}{165}) & \text{Maak de som} \\ &=-b^2+\frac{31}{165}b+(\frac{-4}{33}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(a+\frac{10}{7})(a-\frac{4}{2})& =(\color{red}{a}+\color{orange}{\frac{10}{7}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{10}{7})} . \color{green}{(a)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aa-2a+\frac{10}{7}a-\frac{10}{7}.2& \text{Uitwerken } \\ & =a^2+((-2)+\frac{10}{7})a-(\frac{-20}{7}) & \text{Neem samen} \\ &=a^2-\frac{4}{7}a-(\frac{-20}{7}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-20}{17})(\frac{15}{7}-x)& =(\color{red}{x}+\color{orange}{\frac{-20}{17}}).(\color{green}{-x}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{15}{7}x+\frac{20}{17}x-\frac{20}{17}.\frac{15}{7}& \text{Uitwerken } \\ & =-x^2+(\frac{15}{7}+\frac{20}{17})x-\frac{300}{119} & \text{Neem samen} \\ &=-x^2+\frac{395}{119}x-\frac{300}{119} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-17}{7})(q-\frac{-20}{11})& =(\color{red}{a}+\color{orange}{\frac{-17}{7}}).(\color{green}{q}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{-17}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{7})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{20}{11}a-\frac{17}{7}q-\frac{17}{7}.\frac{20}{11}& \text{Uitwerken } \\ & =aq+\frac{20}{11}a-\frac{17}{7}q-\frac{340}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-10}{18})(\frac{4}{16}-q)& =(\color{red}{b}+\color{orange}{\frac{5}{9}}).(\color{green}{-q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{5}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{4}b-\frac{5}{9}q+\frac{5}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =-bq+\frac{1}{4}b-\frac{5}{9}q+\frac{5}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{1}{8})(\frac{-18}{5}-q)& =(\color{red}{x}+\color{orange}{\frac{-1}{8}}).(\color{green}{-q}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{18}{5}x+\frac{1}{8}q+\frac{1}{8}.\frac{18}{5}& \text{Uitwerken } \\ & =-qx-\frac{18}{5}x+\frac{1}{8}q+\frac{18}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{18}{5}x+\frac{1}{8}q+\frac{9}{20} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{9}-b)(\frac{7}{15}+b)& =(\color{red}{-b}+\color{orange}{\frac{-14}{9}}).(\color{green}{b}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{7}{15}b-\frac{14}{9}b-\frac{14}{9}.\frac{7}{15}& \text{Uitwerken } \\ & =-b^2+((\frac{-7}{15})+(\frac{-14}{9}))b-\frac{98}{135} & \text{Neem samen} \\ &=-b^2-\frac{91}{45}b-\frac{98}{135} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(q-10)(p+\frac{-1}{18})& =(\color{red}{q}+\color{orange}{(-10)}).(\color{green}{p}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(-10)} . \color{green}{(p)} + \color{orange}{(-10)} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{18}q-10p+10.\frac{1}{18}& \text{Uitwerken } \\ & =pq-\frac{1}{18}q-10p+\frac{10}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{1}{18}q-10p+\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{7}{2}+a)(\frac{-11}{15}-x)& =(\color{red}{a}+\color{orange}{\frac{7}{2}}).(\color{green}{-x}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{7}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{15}a-\frac{7}{2}x-\frac{7}{2}.\frac{11}{15}& \text{Uitwerken } \\ & =-ax-\frac{11}{15}a-\frac{7}{2}x-\frac{77}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-17}{18})(\frac{15}{11}-b)& =(\color{red}{a}+\color{orange}{\frac{-17}{18}}).(\color{green}{-b}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{15}{11}a+\frac{17}{18}b-\frac{17}{18}.\frac{15}{11}& \text{Uitwerken } \\ & =-ab+\frac{15}{11}a+\frac{17}{18}b-\frac{255}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{15}{11}a+\frac{17}{18}b-\frac{85}{66} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{12}{17})(\frac{11}{20}+q)& =(\color{red}{x}+\color{orange}{\frac{-12}{17}}).(\color{green}{q}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{-12}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{20}x-\frac{12}{17}q-\frac{12}{17}.\frac{11}{20}& \text{Uitwerken } \\ & =qx+\frac{11}{20}x-\frac{12}{17}q-\frac{132}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{11}{20}x-\frac{12}{17}q-\frac{33}{85} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{10}{19}+x)(a+\frac{-2}{8})& =(\color{red}{x}+\color{orange}{\frac{10}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{10}{19})} . \color{green}{(a)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{4}x+\frac{10}{19}a-\frac{10}{19}.\frac{1}{4}& \text{Uitwerken } \\ & =ax-\frac{1}{4}x+\frac{10}{19}a-\frac{10}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{1}{4}x+\frac{10}{19}a-\frac{5}{38} & \text{Vereenvoudig} \\\end{align}\)
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