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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{10}{17}-x)(b+\frac{-2}{6})& =(\color{red}{-x}+\color{orange}{\frac{10}{17}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{10}{17})} . \color{green}{(b)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{3}x+\frac{10}{17}b-\frac{10}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =-bx+\frac{1}{3}x+\frac{10}{17}b-\frac{10}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}((-13)-a)(a-\frac{-15}{18})& =(\color{red}{-a}+\color{orange}{(-13)}).(\color{green}{a}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(-13)} . \color{green}{(a)} + \color{orange}{(-13)} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{5}{6}a-13a-13.\frac{5}{6}& \text{Uitwerken } \\ & =-a^2+((\frac{-5}{6})+(-13))a-\frac{65}{6} & \text{Neem samen} \\ &=-a^2-\frac{83}{6}a-\frac{65}{6} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(a-16)(\frac{2}{4}-a)& =(\color{red}{a}+\color{orange}{(-16)}).(\color{green}{-a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-16)} . \color{green}{(-a)} + \color{orange}{(-16)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{2}a+16a-16.\frac{1}{2}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{2}+16)a-\frac{16}{2} & \text{Neem samen} \\ &=-a^2+\frac{33}{2}a-\frac{16}{2} & \text{Maak de som} \\ &=-a^2+\frac{33}{2}a-8 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{19}{17}-a)(\frac{6}{10}-a)& =(\color{red}{-a}+\color{orange}{\frac{19}{17}}).(\color{green}{-a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{19}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{5}a-\frac{19}{17}a+\frac{19}{17}.\frac{3}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{5})+(\frac{-19}{17}))a+\frac{57}{85} & \text{Neem samen} \\ &=a^2-\frac{146}{85}a+\frac{57}{85} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{20}{8}-b)(\frac{11}{3}+x)& =(\color{red}{-b}+\color{orange}{\frac{5}{2}}).(\color{green}{x}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{11}{3}b+\frac{5}{2}x+\frac{5}{2}.\frac{11}{3}& \text{Uitwerken } \\ & =-bx-\frac{11}{3}b+\frac{5}{2}x+\frac{55}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-18}{10})(\frac{10}{3}+a)& =(\color{red}{a}+\color{orange}{\frac{9}{5}}).(\color{green}{a}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{9}{5})} . \color{green}{(a)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{10}{3}a+\frac{9}{5}a+\frac{9}{5}.\frac{10}{3}& \text{Uitwerken } \\ & =a^2+(\frac{10}{3}+\frac{9}{5})a+\frac{90}{15} & \text{Neem samen} \\ &=a^2+\frac{77}{15}a+\frac{90}{15} & \text{Maak de som} \\ &=a^2+\frac{77}{15}a+6 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(x-(-19))(a+\frac{16}{8})& =(\color{red}{x}+\color{orange}{19}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(19)} . \color{green}{(a)} + \color{orange}{(19)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2x+19a+19.2& \text{Uitwerken } \\ & =ax+2x+19a+38 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{17}{17})(b-\frac{3}{11})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{11}q-1b+1.\frac{3}{11}& \text{Uitwerken } \\ & =bq-\frac{3}{11}q-1b+\frac{3}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{19}{14}-q)(x-\frac{6}{12})& =(\color{red}{-q}+\color{orange}{\frac{19}{14}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{19}{14})} . \color{green}{(x)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{2}q+\frac{19}{14}x-\frac{19}{14}.\frac{1}{2}& \text{Uitwerken } \\ & =-qx+\frac{1}{2}q+\frac{19}{14}x-\frac{19}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{17}{7}+b)(\frac{-17}{17}-x)& =(\color{red}{b}+\color{orange}{\frac{17}{7}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{17}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bx-1b-\frac{17}{7}x-\frac{17}{7}.1& \text{Uitwerken } \\ & =-bx-1b-\frac{17}{7}x-\frac{17}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{16}{6})(p-\frac{-9}{14})& =(\color{red}{x}+\color{orange}{\frac{8}{3}}).(\color{green}{p}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(\frac{8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{14}x+\frac{8}{3}p+\frac{8}{3}.\frac{9}{14}& \text{Uitwerken } \\ & =px+\frac{9}{14}x+\frac{8}{3}p+\frac{72}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{9}{14}x+\frac{8}{3}p+\frac{12}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-5}{9})(x-\frac{10}{5})& =(\color{red}{p}+\color{orange}{\frac{-5}{9}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-5}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = px-2p-\frac{5}{9}x+\frac{5}{9}.2& \text{Uitwerken } \\ & =px-2p-\frac{5}{9}x+\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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