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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-14}{20})(\frac{6}{12}+b)& =(\color{red}{x}+\color{orange}{\frac{7}{10}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}x+\frac{7}{10}b+\frac{7}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}x+\frac{7}{10}b+\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{16}+p)(\frac{-7}{10}-b)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{-b}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{10}p-\frac{1}{2}b-\frac{1}{2}.\frac{7}{10}& \text{Uitwerken } \\ & =-bp-\frac{7}{10}p-\frac{1}{2}b-\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{14}{15})(\frac{6}{12}-x)& =(\color{red}{p}+\color{orange}{\frac{14}{15}}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{14}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{14}{15})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{2}p-\frac{14}{15}x+\frac{14}{15}.\frac{1}{2}& \text{Uitwerken } \\ & =-px+\frac{1}{2}p-\frac{14}{15}x+\frac{14}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{1}{2}p-\frac{14}{15}x+\frac{7}{15} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{1}{6}-x)(x+\frac{-5}{6})& =(\color{red}{-x}+\color{orange}{\frac{1}{6}}).(\color{green}{x}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{5}{6}x+\frac{1}{6}x-\frac{1}{6}.\frac{5}{6}& \text{Uitwerken } \\ & =-x^2+(\frac{5}{6}+\frac{1}{6})x-\frac{5}{36} & \text{Neem samen} \\ &=-x^2+\frac{6}{6}x-\frac{5}{36} & \text{Maak de som} \\ &=-x^2+1x-\frac{5}{36} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{20}{8}-p)(p+\frac{5}{17})& =(\color{red}{-p}+\color{orange}{\frac{5}{2}}).(\color{green}{p}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{5}{17}p+\frac{5}{2}p+\frac{5}{2}.\frac{5}{17}& \text{Uitwerken } \\ & =-p^2+((\frac{-5}{17})+\frac{5}{2})p+(\frac{-25}{34}) & \text{Neem samen} \\ &=-p^2+\frac{75}{34}p+(\frac{-25}{34}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-3}{14})(q+\frac{-14}{13})& =(\color{red}{b}+\color{orange}{\frac{3}{14}}).(\color{green}{q}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{3}{14})} . \color{green}{(q)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{14}{13}b+\frac{3}{14}q-\frac{3}{14}.\frac{14}{13}& \text{Uitwerken } \\ & =bq-\frac{14}{13}b+\frac{3}{14}q-\frac{42}{182} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{14}{13}b+\frac{3}{14}q-\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-12}{12})(q-\frac{4}{19})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{19}a+1q-1.\frac{4}{19}& \text{Uitwerken } \\ & =aq-\frac{4}{19}a+1q-\frac{4}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{3}{17})(a-\frac{19}{5})& =(\color{red}{a}+\color{orange}{\frac{-3}{17}}).(\color{green}{a}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{-3}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{19}{5}a-\frac{3}{17}a+\frac{3}{17}.\frac{19}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-19}{5})+(\frac{-3}{17}))a+\frac{57}{85} & \text{Neem samen} \\ &=a^2-\frac{338}{85}a+\frac{57}{85} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-17}{19}+a)(\frac{9}{18}-p)& =(\color{red}{a}+\color{orange}{\frac{-17}{19}}).(\color{green}{-p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{2}a+\frac{17}{19}p-\frac{17}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =-ap+\frac{1}{2}a+\frac{17}{19}p-\frac{17}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-18}{5}-x)(q+\frac{18}{5})& =(\color{red}{-x}+\color{orange}{\frac{-18}{5}}).(\color{green}{q}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{18}{5}x-\frac{18}{5}q-\frac{18}{5}.\frac{18}{5}& \text{Uitwerken } \\ & =-qx-\frac{18}{5}x-\frac{18}{5}q-\frac{324}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}((-9)-q)(p-\frac{-13}{8})& =(\color{red}{-q}+\color{orange}{(-9)}).(\color{green}{p}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(-9)} . \color{green}{(p)} + \color{orange}{(-9)} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{13}{8}q-9p-9.\frac{13}{8}& \text{Uitwerken } \\ & =-pq-\frac{13}{8}q-9p-\frac{117}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-6}{17})(p-\frac{11}{7})& =(\color{red}{a}+\color{orange}{\frac{-6}{17}}).(\color{green}{p}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-6}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{7}a-\frac{6}{17}p+\frac{6}{17}.\frac{11}{7}& \text{Uitwerken } \\ & =ap-\frac{11}{7}a-\frac{6}{17}p+\frac{66}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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