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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-14}{18}+a)(\frac{-4}{14}-b)& =(\color{red}{a}+\color{orange}{\frac{-7}{9}}).(\color{green}{-b}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{7}a+\frac{7}{9}b+\frac{7}{9}.\frac{2}{7}& \text{Uitwerken } \\ & =-ab-\frac{2}{7}a+\frac{7}{9}b+\frac{14}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{2}{7}a+\frac{7}{9}b+\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{4}-a)(a+\frac{7}{19})& =(\color{red}{-a}+\color{orange}{\frac{19}{4}}).(\color{green}{a}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{19}{4})} . \color{green}{(a)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{7}{19}a+\frac{19}{4}a+\frac{19}{4}.\frac{7}{19}& \text{Uitwerken } \\ & =-a^2+((\frac{-7}{19})+\frac{19}{4})a+(\frac{-133}{76}) & \text{Neem samen} \\ &=-a^2+\frac{333}{76}a+(\frac{-133}{76}) & \text{Maak de som} \\ &=-a^2+\frac{333}{76}a+(\frac{-7}{4}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(q+\frac{19}{2})(\frac{-8}{19}-a)& =(\color{red}{q}+\color{orange}{\frac{19}{2}}).(\color{green}{-a}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{19}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{8}{19}q-\frac{19}{2}a-\frac{19}{2}.\frac{8}{19}& \text{Uitwerken } \\ & =-aq-\frac{8}{19}q-\frac{19}{2}a-\frac{152}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{8}{19}q-\frac{19}{2}a-4 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-\frac{18}{15})(\frac{19}{15}+a)& =(\color{red}{q}+\color{orange}{\frac{-6}{5}}).(\color{green}{a}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{15}q-\frac{6}{5}a-\frac{6}{5}.\frac{19}{15}& \text{Uitwerken } \\ & =aq+\frac{19}{15}q-\frac{6}{5}a-\frac{114}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{19}{15}q-\frac{6}{5}a-\frac{38}{25} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{12}-x)(p-\frac{7}{12})& =(\color{red}{-x}+\color{orange}{\frac{-5}{4}}).(\color{green}{p}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{12}x-\frac{5}{4}p+\frac{5}{4}.\frac{7}{12}& \text{Uitwerken } \\ & =-px+\frac{7}{12}x-\frac{5}{4}p+\frac{35}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{19}{20}+x)(q+\frac{-6}{19})& =(\color{red}{x}+\color{orange}{\frac{19}{20}}).(\color{green}{q}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{19}{20})} . \color{green}{(q)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{6}{19}x+\frac{19}{20}q-\frac{19}{20}.\frac{6}{19}& \text{Uitwerken } \\ & =qx-\frac{6}{19}x+\frac{19}{20}q-\frac{114}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{6}{19}x+\frac{19}{20}q-\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{12}+a)(q+\frac{-14}{13})& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{14}{13}a+\frac{2}{3}q-\frac{2}{3}.\frac{14}{13}& \text{Uitwerken } \\ & =aq-\frac{14}{13}a+\frac{2}{3}q-\frac{28}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(11-a)(p-\frac{-12}{10})& =(\color{red}{-a}+\color{orange}{11}).(\color{green}{p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(11)} . \color{green}{(p)} + \color{orange}{(11)} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{6}{5}a+11p+11.\frac{6}{5}& \text{Uitwerken } \\ & =-ap-\frac{6}{5}a+11p+\frac{66}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-9}{10}-q)(\frac{20}{14}-p)& =(\color{red}{-q}+\color{orange}{\frac{-9}{10}}).(\color{green}{-p}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{10}{7}q+\frac{9}{10}p-\frac{9}{10}.\frac{10}{7}& \text{Uitwerken } \\ & =pq-\frac{10}{7}q+\frac{9}{10}p-\frac{90}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{10}{7}q+\frac{9}{10}p-\frac{9}{7} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-13}{12})(\frac{14}{9}+p)& =(\color{red}{p}+\color{orange}{\frac{-13}{12}}).(\color{green}{p}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{14}{9}p-\frac{13}{12}p-\frac{13}{12}.\frac{14}{9}& \text{Uitwerken } \\ & =p^2+(\frac{14}{9}+(\frac{-13}{12}))p-(\frac{-182}{108}) & \text{Neem samen} \\ &=p^2+\frac{17}{36}p-(\frac{-182}{108}) & \text{Maak de som} \\ &=p^2+\frac{17}{36}p+\frac{91}{54} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{12}+x)(p+\frac{17}{5})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{5}x+\frac{1}{3}p+\frac{1}{3}.\frac{17}{5}& \text{Uitwerken } \\ & =px+\frac{17}{5}x+\frac{1}{3}p+\frac{17}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-15}{16})(\frac{10}{9}+x)& =(\color{red}{x}+\color{orange}{\frac{-15}{16}}).(\color{green}{x}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{10}{9}x-\frac{15}{16}x-\frac{15}{16}.\frac{10}{9}& \text{Uitwerken } \\ & =x^2+(\frac{10}{9}+(\frac{-15}{16}))x-(\frac{-150}{144}) & \text{Neem samen} \\ &=x^2+\frac{25}{144}x-(\frac{-150}{144}) & \text{Maak de som} \\ &=x^2+\frac{25}{144}x+\frac{25}{24} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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