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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{4}{14})(11+x)& =(\color{red}{x}+\color{orange}{\frac{-2}{7}}).(\color{green}{x}+\color{blue}{11})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(11)} + \color{orange}{(\frac{-2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = xx+11x-\frac{2}{7}x-\frac{2}{7}.11& \text{Uitwerken } \\ & =x^2+(11+(\frac{-2}{7}))x-(\frac{-22}{7}) & \text{Neem samen} \\ &=x^2+\frac{75}{7}x-(\frac{-22}{7}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-2}{6})(\frac{4}{2}-p)& =(\color{red}{a}+\color{orange}{\frac{-1}{3}}).(\color{green}{-p}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ap+2a+\frac{1}{3}p-\frac{1}{3}.2& \text{Uitwerken } \\ & =-ap+2a+\frac{1}{3}p-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(18-x)(\frac{-20}{5}+a)& =(\color{red}{-x}+\color{orange}{18}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(-4)} + \color{orange}{(18)} . \color{green}{(a)} + \color{orange}{(18)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ax+4x+18a-18.4& \text{Uitwerken } \\ & =-ax+4x+18a-72 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-16}{8}+a)(\frac{-14}{8}+a)& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{7}{4}a-2a+2.\frac{7}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-7}{4})+(-2))a+\frac{14}{4} & \text{Neem samen} \\ &=a^2-\frac{15}{4}a+\frac{14}{4} & \text{Maak de som} \\ &=a^2-\frac{15}{4}a+\frac{7}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-6}{14})(\frac{4}{15}+b)& =(\color{red}{q}+\color{orange}{\frac{-3}{7}}).(\color{green}{b}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{15}q-\frac{3}{7}b-\frac{3}{7}.\frac{4}{15}& \text{Uitwerken } \\ & =bq+\frac{4}{15}q-\frac{3}{7}b-\frac{12}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{4}{15}q-\frac{3}{7}b-\frac{4}{35} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+\frac{7}{7})(\frac{2}{4}+q)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{2}q+1q+1.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+(\frac{1}{2}+1)q+\frac{1}{2} & \text{Neem samen} \\ &=q^2+\frac{3}{2}q+\frac{1}{2} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-15}{2}+b)(q+\frac{-2}{15})& =(\color{red}{b}+\color{orange}{\frac{-15}{2}}).(\color{green}{q}+\color{blue}{\frac{-2}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{15})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{-2}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{15}b-\frac{15}{2}q+\frac{15}{2}.\frac{2}{15}& \text{Uitwerken } \\ & =bq-\frac{2}{15}b-\frac{15}{2}q+\frac{30}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{2}{15}b-\frac{15}{2}q+1 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-3}{13})(\frac{6}{13}-b)& =(\color{red}{x}+\color{orange}{\frac{-3}{13}}).(\color{green}{-b}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{6}{13}x+\frac{3}{13}b-\frac{3}{13}.\frac{6}{13}& \text{Uitwerken } \\ & =-bx+\frac{6}{13}x+\frac{3}{13}b-\frac{18}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{19}{18}+a)(\frac{-12}{19}+q)& =(\color{red}{a}+\color{orange}{\frac{19}{18}}).(\color{green}{q}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{19}{18})} . \color{green}{(q)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{12}{19}a+\frac{19}{18}q-\frac{19}{18}.\frac{12}{19}& \text{Uitwerken } \\ & =aq-\frac{12}{19}a+\frac{19}{18}q-\frac{228}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{12}{19}a+\frac{19}{18}q-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{4}{9}-q)(\frac{9}{10}-q)& =(\color{red}{-q}+\color{orange}{\frac{4}{9}}).(\color{green}{-q}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{4}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{9}{10}q-\frac{4}{9}q+\frac{4}{9}.\frac{9}{10}& \text{Uitwerken } \\ & =q^2+((\frac{-9}{10})+(\frac{-4}{9}))q+\frac{36}{90} & \text{Neem samen} \\ &=q^2-\frac{121}{90}q+\frac{36}{90} & \text{Maak de som} \\ &=q^2-\frac{121}{90}q+\frac{2}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-6}{15}+x)(\frac{13}{18}-a)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{-a}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{18}x+\frac{2}{5}a-\frac{2}{5}.\frac{13}{18}& \text{Uitwerken } \\ & =-ax+\frac{13}{18}x+\frac{2}{5}a-\frac{26}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{13}{18}x+\frac{2}{5}a-\frac{13}{45} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{6}{18}+a)(a+\frac{-12}{19})& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{a}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{12}{19}a+\frac{1}{3}a-\frac{1}{3}.\frac{12}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-12}{19})+\frac{1}{3})a-(\frac{-12}{57}) & \text{Neem samen} \\ &=a^2-\frac{17}{57}a-(\frac{-12}{57}) & \text{Maak de som} \\ &=a^2-\frac{17}{57}a+\frac{4}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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