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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-20}{14}-q)(x-\frac{-14}{10})& =(\color{red}{-q}+\color{orange}{\frac{-10}{7}}).(\color{green}{x}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{7}{5}q-\frac{10}{7}x-\frac{10}{7}.\frac{7}{5}& \text{Uitwerken } \\ & =-qx-\frac{7}{5}q-\frac{10}{7}x-\frac{70}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{7}{5}q-\frac{10}{7}x-2 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-18}{17})(x+\frac{-9}{20})& =(\color{red}{q}+\color{orange}{\frac{-18}{17}}).(\color{green}{x}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{20}q-\frac{18}{17}x+\frac{18}{17}.\frac{9}{20}& \text{Uitwerken } \\ & =qx-\frac{9}{20}q-\frac{18}{17}x+\frac{162}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{9}{20}q-\frac{18}{17}x+\frac{81}{170} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{3}{7})(p+\frac{-4}{13})& =(\color{red}{q}+\color{orange}{\frac{3}{7}}).(\color{green}{p}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{13}q+\frac{3}{7}p-\frac{3}{7}.\frac{4}{13}& \text{Uitwerken } \\ & =pq-\frac{4}{13}q+\frac{3}{7}p-\frac{12}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-5}{5}+p)(a+\frac{-13}{18})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{18}p-1a+1.\frac{13}{18}& \text{Uitwerken } \\ & =ap-\frac{13}{18}p-1a+\frac{13}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-6}{12})(\frac{-13}{20}-b)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{-b}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{20}q+\frac{1}{2}b+\frac{1}{2}.\frac{13}{20}& \text{Uitwerken } \\ & =-bq-\frac{13}{20}q+\frac{1}{2}b+\frac{13}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{9}{20}+q)(p+\frac{-5}{5})& =(\color{red}{q}+\color{orange}{\frac{9}{20}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{9}{20})} . \color{green}{(p)} + \color{orange}{(\frac{9}{20})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1q+\frac{9}{20}p-\frac{9}{20}.1& \text{Uitwerken } \\ & =pq-1q+\frac{9}{20}p-\frac{9}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{-7}{4})(\frac{-15}{13}-a)& =(\color{red}{a}+\color{orange}{\frac{-7}{4}}).(\color{green}{-a}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{15}{13}a+\frac{7}{4}a+\frac{7}{4}.\frac{15}{13}& \text{Uitwerken } \\ & =-a^2+((\frac{-15}{13})+\frac{7}{4})a+(\frac{-105}{52}) & \text{Neem samen} \\ &=-a^2+\frac{31}{52}a+(\frac{-105}{52}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(x-\frac{9}{18})(\frac{5}{15}+b)& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{3}x-\frac{1}{2}b-\frac{1}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =bx+\frac{1}{3}x-\frac{1}{2}b-\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{16}{9})(\frac{15}{6}+q)& =(\color{red}{p}+\color{orange}{\frac{-16}{9}}).(\color{green}{q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{2}p-\frac{16}{9}q-\frac{16}{9}.\frac{5}{2}& \text{Uitwerken } \\ & =pq+\frac{5}{2}p-\frac{16}{9}q-\frac{80}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{5}{2}p-\frac{16}{9}q-\frac{40}{9} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-3}{3})(\frac{4}{15}-a)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{4}{15}q-1a+1.\frac{4}{15}& \text{Uitwerken } \\ & =-aq+\frac{4}{15}q-1a+\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{17}{17}+p)(\frac{-15}{18}+a)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{6}p+1a-1.\frac{5}{6}& \text{Uitwerken } \\ & =ap-\frac{5}{6}p+1a-\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{18}{5}-b)(\frac{19}{10}-x)& =(\color{red}{-b}+\color{orange}{\frac{18}{5}}).(\color{green}{-x}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{18}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{10}b-\frac{18}{5}x+\frac{18}{5}.\frac{19}{10}& \text{Uitwerken } \\ & =bx-\frac{19}{10}b-\frac{18}{5}x+\frac{342}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{19}{10}b-\frac{18}{5}x+\frac{171}{25} & \text{Vereenvoudig} \\\end{align}\)
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