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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{9}-a)(\frac{-4}{12}-p)& =(\color{red}{-a}+\color{orange}{\frac{-13}{9}}).(\color{green}{-p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{3}a+\frac{13}{9}p+\frac{13}{9}.\frac{1}{3}& \text{Uitwerken } \\ & =ap+\frac{1}{3}a+\frac{13}{9}p+\frac{13}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-11}{7})(x+\frac{-9}{3})& =(\color{red}{q}+\color{orange}{\frac{11}{7}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(\frac{11}{7})} . \color{green}{(x)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = qx-3q+\frac{11}{7}x-\frac{11}{7}.3& \text{Uitwerken } \\ & =qx-3q+\frac{11}{7}x-\frac{33}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{16}{19})(p-\frac{-11}{11})& =(\color{red}{b}+\color{orange}{\frac{16}{19}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{16}{19})} . \color{green}{(p)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1b+\frac{16}{19}p+\frac{16}{19}.1& \text{Uitwerken } \\ & =bp+1b+\frac{16}{19}p+\frac{16}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{2}{11})(\frac{-5}{2}-q)& =(\color{red}{a}+\color{orange}{\frac{-2}{11}}).(\color{green}{-q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{2}a+\frac{2}{11}q+\frac{2}{11}.\frac{5}{2}& \text{Uitwerken } \\ & =-aq-\frac{5}{2}a+\frac{2}{11}q+\frac{10}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{5}{2}a+\frac{2}{11}q+\frac{5}{11} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{16}+q)(p+\frac{-16}{20})& =(\color{red}{q}+\color{orange}{\frac{5}{8}}).(\color{green}{p}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{5}{8})} . \color{green}{(p)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{5}q+\frac{5}{8}p-\frac{5}{8}.\frac{4}{5}& \text{Uitwerken } \\ & =pq-\frac{4}{5}q+\frac{5}{8}p-\frac{20}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{4}{5}q+\frac{5}{8}p-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+(-9))(p-\frac{14}{6})& =(\color{red}{q}+\color{orange}{(-9)}).(\color{green}{p}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(-9)} . \color{green}{(p)} + \color{orange}{(-9)} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{3}q-9p+9.\frac{7}{3}& \text{Uitwerken } \\ & =pq-\frac{7}{3}q-9p+\frac{63}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{7}{3}q-9p+21 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a-\frac{11}{10})(\frac{-7}{17}+x)& =(\color{red}{a}+\color{orange}{\frac{-11}{10}}).(\color{green}{x}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(\frac{-11}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{17}a-\frac{11}{10}x+\frac{11}{10}.\frac{7}{17}& \text{Uitwerken } \\ & =ax-\frac{7}{17}a-\frac{11}{10}x+\frac{77}{170} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{2}{5})(p+\frac{15}{14})& =(\color{red}{a}+\color{orange}{\frac{2}{5}}).(\color{green}{p}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{15}{14}a+\frac{2}{5}p+\frac{2}{5}.\frac{15}{14}& \text{Uitwerken } \\ & =ap+\frac{15}{14}a+\frac{2}{5}p+\frac{30}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{15}{14}a+\frac{2}{5}p+\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{18}{4})(\frac{8}{17}-p)& =(\color{red}{p}+\color{orange}{\frac{-9}{2}}).(\color{green}{-p}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{8}{17}p+\frac{9}{2}p-\frac{9}{2}.\frac{8}{17}& \text{Uitwerken } \\ & =-p^2+(\frac{8}{17}+\frac{9}{2})p-\frac{72}{34} & \text{Neem samen} \\ &=-p^2+\frac{169}{34}p-\frac{72}{34} & \text{Maak de som} \\ &=-p^2+\frac{169}{34}p-\frac{36}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(q-\frac{19}{11})(\frac{-14}{17}-p)& =(\color{red}{q}+\color{orange}{\frac{-19}{11}}).(\color{green}{-p}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{14}{17}q+\frac{19}{11}p+\frac{19}{11}.\frac{14}{17}& \text{Uitwerken } \\ & =-pq-\frac{14}{17}q+\frac{19}{11}p+\frac{266}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{6}+x)(p+\frac{9}{13})& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{13}x+\frac{5}{3}p+\frac{5}{3}.\frac{9}{13}& \text{Uitwerken } \\ & =px+\frac{9}{13}x+\frac{5}{3}p+\frac{45}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{9}{13}x+\frac{5}{3}p+\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{18}{14}-b)(\frac{13}{13}-q)& =(\color{red}{-b}+\color{orange}{\frac{9}{7}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{9}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq-1b-\frac{9}{7}q+\frac{9}{7}.1& \text{Uitwerken } \\ & =bq-1b-\frac{9}{7}q+\frac{9}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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