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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-5}{18}+q)(q-\frac{9}{6})& =(\color{red}{q}+\color{orange}{\frac{-5}{18}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{3}{2}q-\frac{5}{18}q+\frac{5}{18}.\frac{3}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-3}{2})+(\frac{-5}{18}))q+\frac{15}{36} & \text{Neem samen} \\ &=q^2-\frac{32}{18}q+\frac{15}{36} & \text{Maak de som} \\ &=q^2-\frac{16}{9}q+\frac{5}{12} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-3}{2}+x)(x+\frac{-4}{5})& =(\color{red}{x}+\color{orange}{\frac{-3}{2}}).(\color{green}{x}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{4}{5}x-\frac{3}{2}x+\frac{3}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-4}{5})+(\frac{-3}{2}))x+\frac{12}{10} & \text{Neem samen} \\ &=x^2-\frac{23}{10}x+\frac{12}{10} & \text{Maak de som} \\ &=x^2-\frac{23}{10}x+\frac{6}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(p-\frac{17}{5})(q+\frac{18}{19})& =(\color{red}{p}+\color{orange}{\frac{-17}{5}}).(\color{green}{q}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{18}{19}p-\frac{17}{5}q-\frac{17}{5}.\frac{18}{19}& \text{Uitwerken } \\ & =pq+\frac{18}{19}p-\frac{17}{5}q-\frac{306}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{1}{14})(\frac{-9}{10}+q)& =(\color{red}{x}+\color{orange}{\frac{1}{14}}).(\color{green}{q}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{1}{14})} . \color{green}{(q)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{10}x+\frac{1}{14}q-\frac{1}{14}.\frac{9}{10}& \text{Uitwerken } \\ & =qx-\frac{9}{10}x+\frac{1}{14}q-\frac{9}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{7}{7}+p)(\frac{6}{12}+b)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{2}p+1b+1.\frac{1}{2}& \text{Uitwerken } \\ & =bp+\frac{1}{2}p+1b+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-9}{10})(18-x)& =(\color{red}{b}+\color{orange}{\frac{-9}{10}}).(\color{green}{-x}+\color{blue}{18})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(18)} + \color{orange}{(\frac{-9}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = -bx+18b+\frac{9}{10}x-\frac{9}{10}.18& \text{Uitwerken } \\ & =-bx+18b+\frac{9}{10}x-\frac{162}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+18b+\frac{9}{10}x-\frac{81}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-11}{16})(\frac{-12}{10}-q)& =(\color{red}{x}+\color{orange}{\frac{11}{16}}).(\color{green}{-q}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{11}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{6}{5}x-\frac{11}{16}q-\frac{11}{16}.\frac{6}{5}& \text{Uitwerken } \\ & =-qx-\frac{6}{5}x-\frac{11}{16}q-\frac{66}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{6}{5}x-\frac{11}{16}q-\frac{33}{40} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x+\frac{1}{13})(x+\frac{-16}{9})& =(\color{red}{x}+\color{orange}{\frac{1}{13}}).(\color{green}{x}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{1}{13})} . \color{green}{(x)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{16}{9}x+\frac{1}{13}x-\frac{1}{13}.\frac{16}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-16}{9})+\frac{1}{13})x-(\frac{-16}{117}) & \text{Neem samen} \\ &=x^2-\frac{199}{117}x-(\frac{-16}{117}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(a-\frac{12}{13})(p+\frac{-9}{3})& =(\color{red}{a}+\color{orange}{\frac{-12}{13}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{-12}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ap-3a-\frac{12}{13}p+\frac{12}{13}.3& \text{Uitwerken } \\ & =ap-3a-\frac{12}{13}p+\frac{36}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{6}{19})(\frac{-8}{10}+a)& =(\color{red}{x}+\color{orange}{\frac{6}{19}}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{6}{19})} . \color{green}{(a)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{5}x+\frac{6}{19}a-\frac{6}{19}.\frac{4}{5}& \text{Uitwerken } \\ & =ax-\frac{4}{5}x+\frac{6}{19}a-\frac{24}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{7}{16})(x+\frac{5}{4})& =(\color{red}{a}+\color{orange}{\frac{7}{16}}).(\color{green}{x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{7}{16})} . \color{green}{(x)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{4}a+\frac{7}{16}x+\frac{7}{16}.\frac{5}{4}& \text{Uitwerken } \\ & =ax+\frac{5}{4}a+\frac{7}{16}x+\frac{35}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{16}-p)(b-\frac{18}{13})& =(\color{red}{-p}+\color{orange}{\frac{-5}{8}}).(\color{green}{b}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{18}{13}p-\frac{5}{8}b+\frac{5}{8}.\frac{18}{13}& \text{Uitwerken } \\ & =-bp+\frac{18}{13}p-\frac{5}{8}b+\frac{90}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{18}{13}p-\frac{5}{8}b+\frac{45}{52} & \text{Vereenvoudig} \\\end{align}\)
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