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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-14}{16}+x)(x+\frac{-17}{20})& =(\color{red}{x}+\color{orange}{\frac{-7}{8}}).(\color{green}{x}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{17}{20}x-\frac{7}{8}x+\frac{7}{8}.\frac{17}{20}& \text{Uitwerken } \\ & =x^2+((\frac{-17}{20})+(\frac{-7}{8}))x+\frac{119}{160} & \text{Neem samen} \\ &=x^2-\frac{69}{40}x+\frac{119}{160} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-15}{19})(q-\frac{-13}{12})& =(\color{red}{b}+\color{orange}{\frac{-15}{19}}).(\color{green}{q}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{-15}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{12}b-\frac{15}{19}q-\frac{15}{19}.\frac{13}{12}& \text{Uitwerken } \\ & =bq+\frac{13}{12}b-\frac{15}{19}q-\frac{195}{228} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{13}{12}b-\frac{15}{19}q-\frac{65}{76} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-14}{10})(a-\frac{-14}{18})& =(\color{red}{x}+\color{orange}{\frac{-7}{5}}).(\color{green}{a}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{9}x-\frac{7}{5}a-\frac{7}{5}.\frac{7}{9}& \text{Uitwerken } \\ & =ax+\frac{7}{9}x-\frac{7}{5}a-\frac{49}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-(-14))(a-\frac{-1}{10})& =(\color{red}{b}+\color{orange}{14}).(\color{green}{a}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(14)} . \color{green}{(a)} + \color{orange}{(14)} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{10}b+14a+14.\frac{1}{10}& \text{Uitwerken } \\ & =ab+\frac{1}{10}b+14a+\frac{14}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{10}b+14a+\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{19}+x)(\frac{8}{2}-a)& =(\color{red}{x}+\color{orange}{\frac{16}{19}}).(\color{green}{-a}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(4)} + \color{orange}{(\frac{16}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -ax+4x-\frac{16}{19}a+\frac{16}{19}.4& \text{Uitwerken } \\ & =-ax+4x-\frac{16}{19}a+\frac{64}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{11}{2})(b-\frac{11}{2})& =(\color{red}{b}+\color{orange}{\frac{-11}{2}}).(\color{green}{b}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{-11}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{11}{2}b-\frac{11}{2}b+\frac{11}{2}.\frac{11}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-11}{2})+(\frac{-11}{2}))b+\frac{121}{4} & \text{Neem samen} \\ &=b^2-\frac{22}{2}b+\frac{121}{4} & \text{Maak de som} \\ &=b^2-11b+\frac{121}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(x-\frac{3}{15})(\frac{4}{9}-p)& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{-p}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{4}{9}x+\frac{1}{5}p-\frac{1}{5}.\frac{4}{9}& \text{Uitwerken } \\ & =-px+\frac{4}{9}x+\frac{1}{5}p-\frac{4}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{19}{12}-p)(\frac{11}{8}+q)& =(\color{red}{-p}+\color{orange}{\frac{19}{12}}).(\color{green}{q}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{19}{12})} . \color{green}{(q)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{11}{8}p+\frac{19}{12}q+\frac{19}{12}.\frac{11}{8}& \text{Uitwerken } \\ & =-pq-\frac{11}{8}p+\frac{19}{12}q+\frac{209}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{7}{20})(q+\frac{-18}{17})& =(\color{red}{x}+\color{orange}{\frac{-7}{20}}).(\color{green}{q}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{18}{17}x-\frac{7}{20}q+\frac{7}{20}.\frac{18}{17}& \text{Uitwerken } \\ & =qx-\frac{18}{17}x-\frac{7}{20}q+\frac{126}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{18}{17}x-\frac{7}{20}q+\frac{63}{170} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-13}{10})(p+\frac{2}{14})& =(\color{red}{p}+\color{orange}{\frac{-13}{10}}).(\color{green}{p}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{7}p-\frac{13}{10}p-\frac{13}{10}.\frac{1}{7}& \text{Uitwerken } \\ & =p^2+(\frac{1}{7}+(\frac{-13}{10}))p-(\frac{-13}{70}) & \text{Neem samen} \\ &=p^2-\frac{81}{70}p-(\frac{-13}{70}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(q+\frac{12}{8})(q-\frac{9}{13})& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{9}{13}q+\frac{3}{2}q-\frac{3}{2}.\frac{9}{13}& \text{Uitwerken } \\ & =q^2+((\frac{-9}{13})+\frac{3}{2})q-(\frac{-27}{26}) & \text{Neem samen} \\ &=q^2+\frac{21}{26}q-(\frac{-27}{26}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{5}{17}+q)(p-\frac{-20}{7})& =(\color{red}{q}+\color{orange}{\frac{5}{17}}).(\color{green}{p}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{5}{17})} . \color{green}{(p)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{20}{7}q+\frac{5}{17}p+\frac{5}{17}.\frac{20}{7}& \text{Uitwerken } \\ & =pq+\frac{20}{7}q+\frac{5}{17}p+\frac{100}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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