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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{8}{3}+q)(\frac{-6}{3}-a)& =(\color{red}{q}+\color{orange}{\frac{8}{3}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{8}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -aq-2q-\frac{8}{3}a-\frac{8}{3}.2& \text{Uitwerken } \\ & =-aq-2q-\frac{8}{3}a-\frac{16}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{14}+b)(b-\frac{16}{5})& =(\color{red}{b}+\color{orange}{\frac{4}{7}}).(\color{green}{b}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{4}{7})} . \color{green}{(b)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{16}{5}b+\frac{4}{7}b-\frac{4}{7}.\frac{16}{5}& \text{Uitwerken } \\ & =b^2+((\frac{-16}{5})+\frac{4}{7})b-(\frac{-64}{35}) & \text{Neem samen} \\ &=b^2-\frac{92}{35}b-(\frac{-64}{35}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(a-\frac{9}{13})(\frac{15}{4}+b)& =(\color{red}{a}+\color{orange}{\frac{-9}{13}}).(\color{green}{b}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{15}{4}a-\frac{9}{13}b-\frac{9}{13}.\frac{15}{4}& \text{Uitwerken } \\ & =ab+\frac{15}{4}a-\frac{9}{13}b-\frac{135}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{4}{5}-b)(\frac{-19}{16}-a)& =(\color{red}{-b}+\color{orange}{\frac{4}{5}}).(\color{green}{-a}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{16}b-\frac{4}{5}a-\frac{4}{5}.\frac{19}{16}& \text{Uitwerken } \\ & =ab+\frac{19}{16}b-\frac{4}{5}a-\frac{76}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{19}{16}b-\frac{4}{5}a-\frac{19}{20} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-1}{15}+p)(\frac{-9}{12}-b)& =(\color{red}{p}+\color{orange}{\frac{-1}{15}}).(\color{green}{-b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{4}p+\frac{1}{15}b+\frac{1}{15}.\frac{3}{4}& \text{Uitwerken } \\ & =-bp-\frac{3}{4}p+\frac{1}{15}b+\frac{3}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{3}{4}p+\frac{1}{15}b+\frac{1}{20} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+(-7))(\frac{20}{14}-x)& =(\color{red}{q}+\color{orange}{(-7)}).(\color{green}{-x}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(-7)} . \color{green}{(-x)} + \color{orange}{(-7)} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{10}{7}q+7x-7.\frac{10}{7}& \text{Uitwerken } \\ & =-qx+\frac{10}{7}q+7x-\frac{70}{7} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{10}{7}q+7x-10 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-17}{15}+b)(b+\frac{5}{14})& =(\color{red}{b}+\color{orange}{\frac{-17}{15}}).(\color{green}{b}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{14}b-\frac{17}{15}b-\frac{17}{15}.\frac{5}{14}& \text{Uitwerken } \\ & =b^2+(\frac{5}{14}+(\frac{-17}{15}))b-(\frac{-85}{210}) & \text{Neem samen} \\ &=b^2-\frac{163}{210}b-(\frac{-85}{210}) & \text{Maak de som} \\ &=b^2-\frac{163}{210}b+\frac{17}{42} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-20}{11})(\frac{-12}{8}-q)& =(\color{red}{x}+\color{orange}{\frac{-20}{11}}).(\color{green}{-q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{2}x+\frac{20}{11}q+\frac{20}{11}.\frac{3}{2}& \text{Uitwerken } \\ & =-qx-\frac{3}{2}x+\frac{20}{11}q+\frac{60}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{3}{2}x+\frac{20}{11}q+\frac{30}{11} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-11}{13})(\frac{-17}{16}-x)& =(\color{red}{a}+\color{orange}{\frac{-11}{13}}).(\color{green}{-x}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{17}{16}a+\frac{11}{13}x+\frac{11}{13}.\frac{17}{16}& \text{Uitwerken } \\ & =-ax-\frac{17}{16}a+\frac{11}{13}x+\frac{187}{208} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{2}{16})(\frac{-11}{5}-q)& =(\color{red}{x}+\color{orange}{\frac{1}{8}}).(\color{green}{-q}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{11}{5}x-\frac{1}{8}q-\frac{1}{8}.\frac{11}{5}& \text{Uitwerken } \\ & =-qx-\frac{11}{5}x-\frac{1}{8}q-\frac{11}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-12}{19})(\frac{-11}{7}-q)& =(\color{red}{x}+\color{orange}{\frac{-12}{19}}).(\color{green}{-q}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{11}{7}x+\frac{12}{19}q+\frac{12}{19}.\frac{11}{7}& \text{Uitwerken } \\ & =-qx-\frac{11}{7}x+\frac{12}{19}q+\frac{132}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{19}{16})(x+\frac{-17}{3})& =(\color{red}{b}+\color{orange}{\frac{19}{16}}).(\color{green}{x}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{19}{16})} . \color{green}{(x)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{3}b+\frac{19}{16}x-\frac{19}{16}.\frac{17}{3}& \text{Uitwerken } \\ & =bx-\frac{17}{3}b+\frac{19}{16}x-\frac{323}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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