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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{15}{18})(\frac{-15}{13}-b)& =(\color{red}{x}+\color{orange}{\frac{5}{6}}).(\color{green}{-b}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{15}{13}x-\frac{5}{6}b-\frac{5}{6}.\frac{15}{13}& \text{Uitwerken } \\ & =-bx-\frac{15}{13}x-\frac{5}{6}b-\frac{75}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{15}{13}x-\frac{5}{6}b-\frac{25}{26} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-13}{12}+p)(\frac{19}{15}-x)& =(\color{red}{p}+\color{orange}{\frac{-13}{12}}).(\color{green}{-x}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{19}{15}p+\frac{13}{12}x-\frac{13}{12}.\frac{19}{15}& \text{Uitwerken } \\ & =-px+\frac{19}{15}p+\frac{13}{12}x-\frac{247}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-10}{11}-p)(\frac{-17}{5}+a)& =(\color{red}{-p}+\color{orange}{\frac{-10}{11}}).(\color{green}{a}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{17}{5}p-\frac{10}{11}a+\frac{10}{11}.\frac{17}{5}& \text{Uitwerken } \\ & =-ap+\frac{17}{5}p-\frac{10}{11}a+\frac{170}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{17}{5}p-\frac{10}{11}a+\frac{34}{11} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-15}{2})(x-\frac{-1}{8})& =(\color{red}{p}+\color{orange}{\frac{15}{2}}).(\color{green}{x}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{15}{2})} . \color{green}{(x)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{8}p+\frac{15}{2}x+\frac{15}{2}.\frac{1}{8}& \text{Uitwerken } \\ & =px+\frac{1}{8}p+\frac{15}{2}x+\frac{15}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-18}{14})(\frac{-2}{9}-q)& =(\color{red}{b}+\color{orange}{\frac{9}{7}}).(\color{green}{-q}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{9}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{2}{9}b-\frac{9}{7}q-\frac{9}{7}.\frac{2}{9}& \text{Uitwerken } \\ & =-bq-\frac{2}{9}b-\frac{9}{7}q-\frac{18}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{2}{9}b-\frac{9}{7}q-\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-17}{2})(p+\frac{3}{17})& =(\color{red}{x}+\color{orange}{\frac{17}{2}}).(\color{green}{p}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{17}{2})} . \color{green}{(p)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{17}x+\frac{17}{2}p+\frac{17}{2}.\frac{3}{17}& \text{Uitwerken } \\ & =px+\frac{3}{17}x+\frac{17}{2}p+\frac{51}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{3}{17}x+\frac{17}{2}p+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-15}{19}-b)(x+\frac{6}{19})& =(\color{red}{-b}+\color{orange}{\frac{-15}{19}}).(\color{green}{x}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{-15}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{6}{19}b-\frac{15}{19}x-\frac{15}{19}.\frac{6}{19}& \text{Uitwerken } \\ & =-bx-\frac{6}{19}b-\frac{15}{19}x-\frac{90}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-8}{16}-q)(b+\frac{6}{11})& =(\color{red}{-q}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{6}{11}q-\frac{1}{2}b-\frac{1}{2}.\frac{6}{11}& \text{Uitwerken } \\ & =-bq-\frac{6}{11}q-\frac{1}{2}b-\frac{6}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{6}{11}q-\frac{1}{2}b-\frac{3}{11} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-19}{3})(x+\frac{-2}{3})& =(\color{red}{b}+\color{orange}{\frac{-19}{3}}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{3}b-\frac{19}{3}x+\frac{19}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =bx-\frac{2}{3}b-\frac{19}{3}x+\frac{38}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{17}{12}+q)(\frac{-3}{6}+x)& =(\color{red}{q}+\color{orange}{\frac{17}{12}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{17}{12})} . \color{green}{(x)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{2}q+\frac{17}{12}x-\frac{17}{12}.\frac{1}{2}& \text{Uitwerken } \\ & =qx-\frac{1}{2}q+\frac{17}{12}x-\frac{17}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{17}{14})(b+\frac{17}{7})& =(\color{red}{a}+\color{orange}{\frac{17}{14}}).(\color{green}{b}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{17}{14})} . \color{green}{(b)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{7}a+\frac{17}{14}b+\frac{17}{14}.\frac{17}{7}& \text{Uitwerken } \\ & =ab+\frac{17}{7}a+\frac{17}{14}b+\frac{289}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-15}{16})(p+\frac{-1}{6})& =(\color{red}{q}+\color{orange}{\frac{-15}{16}}).(\color{green}{p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{6}q-\frac{15}{16}p+\frac{15}{16}.\frac{1}{6}& \text{Uitwerken } \\ & =pq-\frac{1}{6}q-\frac{15}{16}p+\frac{15}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{1}{6}q-\frac{15}{16}p+\frac{5}{32} & \text{Vereenvoudig} \\\end{align}\)
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