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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{12}{12}-q)(\frac{2}{17}-q)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{2}{17}q-1q+1.\frac{2}{17}& \text{Uitwerken } \\ & =q^2+((\frac{-2}{17})+(-1))q+\frac{2}{17} & \text{Neem samen} \\ &=q^2-\frac{19}{17}q+\frac{2}{17} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-8}{7}+q)(b-\frac{10}{13})& =(\color{red}{q}+\color{orange}{\frac{-8}{7}}).(\color{green}{b}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{10}{13}q-\frac{8}{7}b+\frac{8}{7}.\frac{10}{13}& \text{Uitwerken } \\ & =bq-\frac{10}{13}q-\frac{8}{7}b+\frac{80}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-15}{9}-q)(q+\frac{17}{5})& =(\color{red}{-q}+\color{orange}{\frac{-5}{3}}).(\color{green}{q}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{17}{5}q-\frac{5}{3}q-\frac{5}{3}.\frac{17}{5}& \text{Uitwerken } \\ & =-q^2+((\frac{-17}{5})+(\frac{-5}{3}))q-\frac{85}{15} & \text{Neem samen} \\ &=-q^2-\frac{76}{15}q-\frac{85}{15} & \text{Maak de som} \\ &=-q^2-\frac{76}{15}q-\frac{17}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-11}{14})(\frac{-19}{17}-b)& =(\color{red}{x}+\color{orange}{\frac{-11}{14}}).(\color{green}{-b}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{19}{17}x+\frac{11}{14}b+\frac{11}{14}.\frac{19}{17}& \text{Uitwerken } \\ & =-bx-\frac{19}{17}x+\frac{11}{14}b+\frac{209}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{17}{18})(x+\frac{17}{14})& =(\color{red}{b}+\color{orange}{\frac{-17}{18}}).(\color{green}{x}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{14}b-\frac{17}{18}x-\frac{17}{18}.\frac{17}{14}& \text{Uitwerken } \\ & =bx+\frac{17}{14}b-\frac{17}{18}x-\frac{289}{252} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-9}{5})(x+\frac{18}{16})& =(\color{red}{q}+\color{orange}{\frac{9}{5}}).(\color{green}{x}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{9}{5})} . \color{green}{(x)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{8}q+\frac{9}{5}x+\frac{9}{5}.\frac{9}{8}& \text{Uitwerken } \\ & =qx+\frac{9}{8}q+\frac{9}{5}x+\frac{81}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{1}{14})(\frac{-2}{13}-p)& =(\color{red}{q}+\color{orange}{\frac{1}{14}}).(\color{green}{-p}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{1}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{13}q-\frac{1}{14}p-\frac{1}{14}.\frac{2}{13}& \text{Uitwerken } \\ & =-pq-\frac{2}{13}q-\frac{1}{14}p-\frac{2}{182} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{2}{13}q-\frac{1}{14}p-\frac{1}{91} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{17}{16}-p)(\frac{10}{14}+x)& =(\color{red}{-p}+\color{orange}{\frac{17}{16}}).(\color{green}{x}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{17}{16})} . \color{green}{(x)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{5}{7}p+\frac{17}{16}x+\frac{17}{16}.\frac{5}{7}& \text{Uitwerken } \\ & =-px-\frac{5}{7}p+\frac{17}{16}x+\frac{85}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-3}{9})(p-\frac{7}{8})& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{8}a+\frac{1}{3}p-\frac{1}{3}.\frac{7}{8}& \text{Uitwerken } \\ & =ap-\frac{7}{8}a+\frac{1}{3}p-\frac{7}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-19}{9}+p)(b+\frac{18}{5})& =(\color{red}{p}+\color{orange}{\frac{-19}{9}}).(\color{green}{b}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{18}{5}p-\frac{19}{9}b-\frac{19}{9}.\frac{18}{5}& \text{Uitwerken } \\ & =bp+\frac{18}{5}p-\frac{19}{9}b-\frac{342}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{18}{5}p-\frac{19}{9}b-\frac{38}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-5}{18}+a)(\frac{6}{17}+b)& =(\color{red}{a}+\color{orange}{\frac{-5}{18}}).(\color{green}{b}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{6}{17}a-\frac{5}{18}b-\frac{5}{18}.\frac{6}{17}& \text{Uitwerken } \\ & =ab+\frac{6}{17}a-\frac{5}{18}b-\frac{30}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{6}{17}a-\frac{5}{18}b-\frac{5}{51} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-7}{18})(x-\frac{-9}{6})& =(\color{red}{b}+\color{orange}{\frac{7}{18}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{7}{18})} . \color{green}{(x)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{2}b+\frac{7}{18}x+\frac{7}{18}.\frac{3}{2}& \text{Uitwerken } \\ & =bx+\frac{3}{2}b+\frac{7}{18}x+\frac{21}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{2}b+\frac{7}{18}x+\frac{7}{12} & \text{Vereenvoudig} \\\end{align}\)
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