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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{7}-p)(p-\frac{14}{6})& =(\color{red}{-p}+\color{orange}{\frac{-19}{7}}).(\color{green}{p}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{7}{3}p-\frac{19}{7}p+\frac{19}{7}.\frac{7}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{7}{3}+(\frac{-19}{7}))p+(\frac{-133}{21}) & \text{Neem samen} \\ &=-p^2-\frac{8}{21}p+(\frac{-133}{21}) & \text{Maak de som} \\ &=-p^2-\frac{8}{21}p+(\frac{-19}{3}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(a-\frac{3}{8})(\frac{-1}{8}+p)& =(\color{red}{a}+\color{orange}{\frac{-3}{8}}).(\color{green}{p}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{8}a-\frac{3}{8}p+\frac{3}{8}.\frac{1}{8}& \text{Uitwerken } \\ & =ap-\frac{1}{8}a-\frac{3}{8}p+\frac{3}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{4}+a)(p+\frac{16}{13})& =(\color{red}{a}+\color{orange}{\frac{-11}{4}}).(\color{green}{p}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(\frac{-11}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{4})} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{13}a-\frac{11}{4}p-\frac{11}{4}.\frac{16}{13}& \text{Uitwerken } \\ & =ap+\frac{16}{13}a-\frac{11}{4}p-\frac{176}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{16}{13}a-\frac{11}{4}p-\frac{44}{13} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{16}{8})(b-\frac{1}{6})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{6}x+2b-2.\frac{1}{6}& \text{Uitwerken } \\ & =bx-\frac{1}{6}x+2b-\frac{2}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{6}x+2b-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{18}{15}+a)((-20)-x)& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{-x}+\color{blue}{(-20)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(-20)} + \color{orange}{(\frac{6}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = -ax-20a-\frac{6}{5}x-\frac{6}{5}.20& \text{Uitwerken } \\ & =-ax-20a-\frac{6}{5}x-\frac{120}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-20a-\frac{6}{5}x-24 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-7}{4})(x+\frac{-18}{7})& =(\color{red}{x}+\color{orange}{\frac{-7}{4}}).(\color{green}{x}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{18}{7}x-\frac{7}{4}x+\frac{7}{4}.\frac{18}{7}& \text{Uitwerken } \\ & =x^2+((\frac{-18}{7})+(\frac{-7}{4}))x+\frac{126}{28} & \text{Neem samen} \\ &=x^2-\frac{121}{28}x+\frac{126}{28} & \text{Maak de som} \\ &=x^2-\frac{121}{28}x+\frac{9}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{10}+b)(q-\frac{-8}{16})& =(\color{red}{b}+\color{orange}{\frac{-7}{5}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{2}b-\frac{7}{5}q-\frac{7}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =bq+\frac{1}{2}b-\frac{7}{5}q-\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{3}{14})(\frac{14}{4}+p)& =(\color{red}{p}+\color{orange}{\frac{-3}{14}}).(\color{green}{p}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{-3}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{14})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{7}{2}p-\frac{3}{14}p-\frac{3}{14}.\frac{7}{2}& \text{Uitwerken } \\ & =p^2+(\frac{7}{2}+(\frac{-3}{14}))p-(\frac{-21}{28}) & \text{Neem samen} \\ &=p^2+\frac{46}{14}p-(\frac{-21}{28}) & \text{Maak de som} \\ &=p^2+\frac{23}{7}p+\frac{3}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(q+\frac{10}{7})(\frac{-13}{13}-p)& =(\color{red}{q}+\color{orange}{\frac{10}{7}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{10}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pq-1q-\frac{10}{7}p-\frac{10}{7}.1& \text{Uitwerken } \\ & =-pq-1q-\frac{10}{7}p-\frac{10}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-12}{16}-a)(\frac{19}{20}+q)& =(\color{red}{-a}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{20}a-\frac{3}{4}q-\frac{3}{4}.\frac{19}{20}& \text{Uitwerken } \\ & =-aq-\frac{19}{20}a-\frac{3}{4}q-\frac{57}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{14}{5})(17+q)& =(\color{red}{b}+\color{orange}{\frac{-14}{5}}).(\color{green}{q}+\color{blue}{17})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(17)} + \color{orange}{(\frac{-14}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = bq+17b-\frac{14}{5}q-\frac{14}{5}.17& \text{Uitwerken } \\ & =bq+17b-\frac{14}{5}q-\frac{238}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{19}{2}-b)(\frac{14}{19}-x)& =(\color{red}{-b}+\color{orange}{\frac{19}{2}}).(\color{green}{-x}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(\frac{19}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{14}{19}b-\frac{19}{2}x+\frac{19}{2}.\frac{14}{19}& \text{Uitwerken } \\ & =bx-\frac{14}{19}b-\frac{19}{2}x+\frac{266}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{14}{19}b-\frac{19}{2}x+7 & \text{Vereenvoudig} \\\end{align}\)
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