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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-6}{2}-b)(x+\frac{-11}{3})& =(\color{red}{-b}+\color{orange}{(-3)}).(\color{green}{x}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(-3)} . \color{green}{(x)} + \color{orange}{(-3)} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{11}{3}b-3x+3.\frac{11}{3}& \text{Uitwerken } \\ & =-bx+\frac{11}{3}b-3x+\frac{33}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{11}{3}b-3x+11 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-18}{13})(\frac{-3}{4}+a)& =(\color{red}{a}+\color{orange}{\frac{18}{13}}).(\color{green}{a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{18}{13})} . \color{green}{(a)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{4}a+\frac{18}{13}a-\frac{18}{13}.\frac{3}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{4})+\frac{18}{13})a-(\frac{-54}{52}) & \text{Neem samen} \\ &=a^2+\frac{33}{52}a-(\frac{-54}{52}) & \text{Maak de som} \\ &=a^2+\frac{33}{52}a+\frac{27}{26} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{14}{7}+q)(\frac{-15}{11}+q)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{15}{11}q+2q-2.\frac{15}{11}& \text{Uitwerken } \\ & =q^2+((\frac{-15}{11})+2)q-(\frac{-30}{11}) & \text{Neem samen} \\ &=q^2+\frac{7}{11}q-(\frac{-30}{11}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a+\frac{9}{19})(\frac{-12}{4}-a)& =(\color{red}{a}+\color{orange}{\frac{9}{19}}).(\color{green}{-a}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{9}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -aa-3a-\frac{9}{19}a-\frac{9}{19}.3& \text{Uitwerken } \\ & =-a^2+((-3)+(\frac{-9}{19}))a-\frac{27}{19} & \text{Neem samen} \\ &=-a^2-\frac{66}{19}a-\frac{27}{19} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-19}{8})(p+\frac{-2}{12})& =(\color{red}{a}+\color{orange}{\frac{-19}{8}}).(\color{green}{p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-19}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{6}a-\frac{19}{8}p+\frac{19}{8}.\frac{1}{6}& \text{Uitwerken } \\ & =ap-\frac{1}{6}a-\frac{19}{8}p+\frac{19}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(15+b)(\frac{6}{12}+b)& =(\color{red}{b}+\color{orange}{15}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(15)} . \color{green}{(b)} + \color{orange}{(15)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{2}b+15b+15.\frac{1}{2}& \text{Uitwerken } \\ & =b^2+(\frac{1}{2}+15)b+\frac{15}{2} & \text{Neem samen} \\ &=b^2+\frac{31}{2}b+\frac{15}{2} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-19}{2}-q)(\frac{3}{10}-q)& =(\color{red}{-q}+\color{orange}{\frac{-19}{2}}).(\color{green}{-q}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{3}{10}q+\frac{19}{2}q-\frac{19}{2}.\frac{3}{10}& \text{Uitwerken } \\ & =q^2+((\frac{-3}{10})+\frac{19}{2})q-(\frac{-57}{20}) & \text{Neem samen} \\ &=q^2+\frac{92}{10}q-(\frac{-57}{20}) & \text{Maak de som} \\ &=q^2+\frac{46}{5}q+\frac{57}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(\frac{-14}{11}+p)(\frac{-4}{18}+x)& =(\color{red}{p}+\color{orange}{\frac{-14}{11}}).(\color{green}{x}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{9}p-\frac{14}{11}x+\frac{14}{11}.\frac{2}{9}& \text{Uitwerken } \\ & =px-\frac{2}{9}p-\frac{14}{11}x+\frac{28}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{-8}{5})(\frac{3}{15}+a)& =(\color{red}{q}+\color{orange}{\frac{-8}{5}}).(\color{green}{a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{5}q-\frac{8}{5}a-\frac{8}{5}.\frac{1}{5}& \text{Uitwerken } \\ & =aq+\frac{1}{5}q-\frac{8}{5}a-\frac{8}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-4}{16}+x)(p-\frac{15}{15})& =(\color{red}{x}+\color{orange}{\frac{-1}{4}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1x-\frac{1}{4}p+\frac{1}{4}.1& \text{Uitwerken } \\ & =px-1x-\frac{1}{4}p+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-20}{12}+q)(\frac{20}{7}+b)& =(\color{red}{q}+\color{orange}{\frac{-5}{3}}).(\color{green}{b}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{20}{7}q-\frac{5}{3}b-\frac{5}{3}.\frac{20}{7}& \text{Uitwerken } \\ & =bq+\frac{20}{7}q-\frac{5}{3}b-\frac{100}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-4}{20}-q)(b-\frac{-14}{8})& =(\color{red}{-q}+\color{orange}{\frac{-1}{5}}).(\color{green}{b}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{4}q-\frac{1}{5}b-\frac{1}{5}.\frac{7}{4}& \text{Uitwerken } \\ & =-bq-\frac{7}{4}q-\frac{1}{5}b-\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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