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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{13}{14})(x-\frac{4}{18})& =(\color{red}{x}+\color{orange}{\frac{13}{14}}).(\color{green}{x}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{13}{14})} . \color{green}{(x)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{2}{9}x+\frac{13}{14}x-\frac{13}{14}.\frac{2}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-2}{9})+\frac{13}{14})x-(\frac{-26}{126}) & \text{Neem samen} \\ &=x^2+\frac{89}{126}x-(\frac{-26}{126}) & \text{Maak de som} \\ &=x^2+\frac{89}{126}x+\frac{13}{63} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(\frac{18}{7}-p)(b-\frac{-11}{15})& =(\color{red}{-p}+\color{orange}{\frac{18}{7}}).(\color{green}{b}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{18}{7})} . \color{green}{(b)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{11}{15}p+\frac{18}{7}b+\frac{18}{7}.\frac{11}{15}& \text{Uitwerken } \\ & =-bp-\frac{11}{15}p+\frac{18}{7}b+\frac{198}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{11}{15}p+\frac{18}{7}b+\frac{66}{35} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-16}{8})(17-q)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{-q}+\color{blue}{17})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(17)} + \color{orange}{(2)} . \color{green}{(-q)} + \color{orange}{(2)} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = -qq+17q-2q+2.17& \text{Uitwerken } \\ & =-q^2+(17+(-2))q+(-34) & \text{Neem samen} \\ &=-q^2+15q+(-34) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-16}{3}-b)(\frac{-5}{12}-x)& =(\color{red}{-b}+\color{orange}{\frac{-16}{3}}).(\color{green}{-x}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{-16}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{12}b+\frac{16}{3}x+\frac{16}{3}.\frac{5}{12}& \text{Uitwerken } \\ & =bx+\frac{5}{12}b+\frac{16}{3}x+\frac{80}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{5}{12}b+\frac{16}{3}x+\frac{20}{9} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-15}{12})(\frac{6}{16}+p)& =(\color{red}{q}+\color{orange}{\frac{-5}{4}}).(\color{green}{p}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{8}q-\frac{5}{4}p-\frac{5}{4}.\frac{3}{8}& \text{Uitwerken } \\ & =pq+\frac{3}{8}q-\frac{5}{4}p-\frac{15}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-2}{12}-b)(\frac{17}{12}+q)& =(\color{red}{-b}+\color{orange}{\frac{-1}{6}}).(\color{green}{q}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{17}{12}b-\frac{1}{6}q-\frac{1}{6}.\frac{17}{12}& \text{Uitwerken } \\ & =-bq-\frac{17}{12}b-\frac{1}{6}q-\frac{17}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-14}{8})(\frac{5}{12}+a)& =(\color{red}{p}+\color{orange}{\frac{7}{4}}).(\color{green}{a}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{12}p+\frac{7}{4}a+\frac{7}{4}.\frac{5}{12}& \text{Uitwerken } \\ & =ap+\frac{5}{12}p+\frac{7}{4}a+\frac{35}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-1}{11}+b)(x+\frac{-19}{8})& =(\color{red}{b}+\color{orange}{\frac{-1}{11}}).(\color{green}{x}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{8}b-\frac{1}{11}x+\frac{1}{11}.\frac{19}{8}& \text{Uitwerken } \\ & =bx-\frac{19}{8}b-\frac{1}{11}x+\frac{19}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-7}{6}+p)(\frac{-15}{5}+x)& =(\color{red}{p}+\color{orange}{\frac{-7}{6}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{-7}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = px-3p-\frac{7}{6}x+\frac{7}{6}.3& \text{Uitwerken } \\ & =px-3p-\frac{7}{6}x+\frac{21}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-3p-\frac{7}{6}x+\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-8}{10})(q+\frac{17}{4})& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{q}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{4}x+\frac{4}{5}q+\frac{4}{5}.\frac{17}{4}& \text{Uitwerken } \\ & =qx+\frac{17}{4}x+\frac{4}{5}q+\frac{68}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{17}{4}x+\frac{4}{5}q+\frac{17}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a+\frac{-19}{12})(\frac{-15}{13}+p)& =(\color{red}{a}+\color{orange}{\frac{-19}{12}}).(\color{green}{p}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{15}{13}a-\frac{19}{12}p+\frac{19}{12}.\frac{15}{13}& \text{Uitwerken } \\ & =ap-\frac{15}{13}a-\frac{19}{12}p+\frac{285}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{15}{13}a-\frac{19}{12}p+\frac{95}{52} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-20}{11}-a)(\frac{9}{4}-x)& =(\color{red}{-a}+\color{orange}{\frac{-20}{11}}).(\color{green}{-x}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{4}a+\frac{20}{11}x-\frac{20}{11}.\frac{9}{4}& \text{Uitwerken } \\ & =ax-\frac{9}{4}a+\frac{20}{11}x-\frac{180}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{9}{4}a+\frac{20}{11}x-\frac{45}{11} & \text{Vereenvoudig} \\\end{align}\)
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