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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{2}{16}+x)(\frac{10}{10}-x)& =(\color{red}{x}+\color{orange}{\frac{1}{8}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -xx+1x-\frac{1}{8}x+\frac{1}{8}.1& \text{Uitwerken } \\ & =-x^2+(1+(\frac{-1}{8}))x+(\frac{-1}{8}) & \text{Neem samen} \\ &=-x^2+\frac{7}{8}x+(\frac{-1}{8}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{17}{10}+q)(\frac{12}{5}+a)& =(\color{red}{q}+\color{orange}{\frac{17}{10}}).(\color{green}{a}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{17}{10})} . \color{green}{(a)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{12}{5}q+\frac{17}{10}a+\frac{17}{10}.\frac{12}{5}& \text{Uitwerken } \\ & =aq+\frac{12}{5}q+\frac{17}{10}a+\frac{204}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{12}{5}q+\frac{17}{10}a+\frac{102}{25} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-6}{12})(q-\frac{-14}{16})& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{8}a+\frac{1}{2}q+\frac{1}{2}.\frac{7}{8}& \text{Uitwerken } \\ & =aq+\frac{7}{8}a+\frac{1}{2}q+\frac{7}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{14}+p)(x-\frac{-6}{9})& =(\color{red}{p}+\color{orange}{\frac{9}{14}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{9}{14})} . \color{green}{(x)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{2}{3}p+\frac{9}{14}x+\frac{9}{14}.\frac{2}{3}& \text{Uitwerken } \\ & =px+\frac{2}{3}p+\frac{9}{14}x+\frac{18}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{2}{3}p+\frac{9}{14}x+\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{13}-q)(p-\frac{-4}{11})& =(\color{red}{-q}+\color{orange}{\frac{-9}{13}}).(\color{green}{p}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{4}{11}q-\frac{9}{13}p-\frac{9}{13}.\frac{4}{11}& \text{Uitwerken } \\ & =-pq-\frac{4}{11}q-\frac{9}{13}p-\frac{36}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-3}{6})(x+\frac{-5}{12})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{12}p+\frac{1}{2}x-\frac{1}{2}.\frac{5}{12}& \text{Uitwerken } \\ & =px-\frac{5}{12}p+\frac{1}{2}x-\frac{5}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{14}{8}-x)(p+\frac{4}{8})& =(\color{red}{-x}+\color{orange}{\frac{7}{4}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{7}{4})} . \color{green}{(p)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{2}x+\frac{7}{4}p+\frac{7}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =-px-\frac{1}{2}x+\frac{7}{4}p+\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-5}{8}-p)(\frac{17}{13}-x)& =(\color{red}{-p}+\color{orange}{\frac{-5}{8}}).(\color{green}{-x}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{13}p+\frac{5}{8}x-\frac{5}{8}.\frac{17}{13}& \text{Uitwerken } \\ & =px-\frac{17}{13}p+\frac{5}{8}x-\frac{85}{104} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{14}{10})(p+\frac{-4}{8})& =(\color{red}{p}+\color{orange}{\frac{-7}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{2}p-\frac{7}{5}p+\frac{7}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{2})+(\frac{-7}{5}))p+\frac{7}{10} & \text{Neem samen} \\ &=p^2-\frac{19}{10}p+\frac{7}{10} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{17}{17}-q)(p-(-11))& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{11})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(11)} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = -pq-11q+1p+1.11& \text{Uitwerken } \\ & =-pq-11q+1p+11 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{10}{12})(a-\frac{17}{15})& =(\color{red}{b}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{17}{15}b-\frac{5}{6}a+\frac{5}{6}.\frac{17}{15}& \text{Uitwerken } \\ & =ab-\frac{17}{15}b-\frac{5}{6}a+\frac{85}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{17}{15}b-\frac{5}{6}a+\frac{17}{18} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{12}+p)(x-\frac{20}{13})& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{20}{13}p+\frac{3}{4}x-\frac{3}{4}.\frac{20}{13}& \text{Uitwerken } \\ & =px-\frac{20}{13}p+\frac{3}{4}x-\frac{60}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{20}{13}p+\frac{3}{4}x-\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
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