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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{14}{11})(1-q)& =(\color{red}{a}+\color{orange}{\frac{14}{11}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{14}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -aq+1a-\frac{14}{11}q+\frac{14}{11}.1& \text{Uitwerken } \\ & =-aq+1a-\frac{14}{11}q+\frac{14}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-15}{20}-p)(b-\frac{-20}{19})& =(\color{red}{-p}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{20}{19}p-\frac{3}{4}b-\frac{3}{4}.\frac{20}{19}& \text{Uitwerken } \\ & =-bp-\frac{20}{19}p-\frac{3}{4}b-\frac{60}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{20}{19}p-\frac{3}{4}b-\frac{15}{19} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+\frac{6}{18})(\frac{17}{8}+q)& =(\color{red}{b}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{8}b+\frac{1}{3}q+\frac{1}{3}.\frac{17}{8}& \text{Uitwerken } \\ & =bq+\frac{17}{8}b+\frac{1}{3}q+\frac{17}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{4}{9})(\frac{17}{10}-a)& =(\color{red}{a}+\color{orange}{\frac{-4}{9}}).(\color{green}{-a}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{17}{10}a+\frac{4}{9}a-\frac{4}{9}.\frac{17}{10}& \text{Uitwerken } \\ & =-a^2+(\frac{17}{10}+\frac{4}{9})a-\frac{68}{90} & \text{Neem samen} \\ &=-a^2+\frac{193}{90}a-\frac{68}{90} & \text{Maak de som} \\ &=-a^2+\frac{193}{90}a-\frac{34}{45} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-7}{7})(\frac{-1}{18}+b)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{18}p+1b-1.\frac{1}{18}& \text{Uitwerken } \\ & =bp-\frac{1}{18}p+1b-\frac{1}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-5}{12})(b-\frac{15}{2})& =(\color{red}{x}+\color{orange}{\frac{-5}{12}}).(\color{green}{b}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-5}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{12})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{15}{2}x-\frac{5}{12}b+\frac{5}{12}.\frac{15}{2}& \text{Uitwerken } \\ & =bx-\frac{15}{2}x-\frac{5}{12}b+\frac{75}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{15}{2}x-\frac{5}{12}b+\frac{25}{8} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{17}{4})(a-\frac{-3}{13})& =(\color{red}{p}+\color{orange}{\frac{-17}{4}}).(\color{green}{a}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{13}p-\frac{17}{4}a-\frac{17}{4}.\frac{3}{13}& \text{Uitwerken } \\ & =ap+\frac{3}{13}p-\frac{17}{4}a-\frac{51}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{3}{8}+x)(p-\frac{-19}{12})& =(\color{red}{x}+\color{orange}{\frac{3}{8}}).(\color{green}{p}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{3}{8})} . \color{green}{(p)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{19}{12}x+\frac{3}{8}p+\frac{3}{8}.\frac{19}{12}& \text{Uitwerken } \\ & =px+\frac{19}{12}x+\frac{3}{8}p+\frac{57}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{19}{12}x+\frac{3}{8}p+\frac{19}{32} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-17}{13})(\frac{16}{14}-a)& =(\color{red}{a}+\color{orange}{\frac{-17}{13}}).(\color{green}{-a}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-17}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{8}{7}a+\frac{17}{13}a-\frac{17}{13}.\frac{8}{7}& \text{Uitwerken } \\ & =-a^2+(\frac{8}{7}+\frac{17}{13})a-\frac{136}{91} & \text{Neem samen} \\ &=-a^2+\frac{223}{91}a-\frac{136}{91} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{14}{7}-b)(\frac{5}{11}-x)& =(\color{red}{-b}+\color{orange}{2}).(\color{green}{-x}+\color{blue}{\frac{5}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{11})} + \color{orange}{(2)} . \color{green}{(-x)} + \color{orange}{(2)} . \color{blue}{(\frac{5}{11})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{11}b-2x+2.\frac{5}{11}& \text{Uitwerken } \\ & =bx-\frac{5}{11}b-2x+\frac{10}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{12}{8}+x)(\frac{18}{11}+a)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{18}{11}x+\frac{3}{2}a+\frac{3}{2}.\frac{18}{11}& \text{Uitwerken } \\ & =ax+\frac{18}{11}x+\frac{3}{2}a+\frac{54}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{18}{11}x+\frac{3}{2}a+\frac{27}{11} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-7}{5}+q)(\frac{20}{3}+a)& =(\color{red}{q}+\color{orange}{\frac{-7}{5}}).(\color{green}{a}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{20}{3}q-\frac{7}{5}a-\frac{7}{5}.\frac{20}{3}& \text{Uitwerken } \\ & =aq+\frac{20}{3}q-\frac{7}{5}a-\frac{140}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{20}{3}q-\frac{7}{5}a-\frac{28}{3} & \text{Vereenvoudig} \\\end{align}\)
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