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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(19+p)(\frac{1}{7}+q)& =(\color{red}{p}+\color{orange}{19}).(\color{green}{q}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(19)} . \color{green}{(q)} + \color{orange}{(19)} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{7}p+19q+19.\frac{1}{7}& \text{Uitwerken } \\ & =pq+\frac{1}{7}p+19q+\frac{19}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{13}{15})(q+\frac{-11}{15})& =(\color{red}{q}+\color{orange}{\frac{13}{15}}).(\color{green}{q}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{13}{15})} . \color{green}{(q)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{15}q+\frac{13}{15}q-\frac{13}{15}.\frac{11}{15}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{15})+\frac{13}{15})q-(\frac{-143}{225}) & \text{Neem samen} \\ &=q^2+\frac{2}{15}q-(\frac{-143}{225}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-13}{2}-b)(b-\frac{-5}{14})& =(\color{red}{-b}+\color{orange}{\frac{-13}{2}}).(\color{green}{b}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{5}{14}b-\frac{13}{2}b-\frac{13}{2}.\frac{5}{14}& \text{Uitwerken } \\ & =-b^2+((\frac{-5}{14})+(\frac{-13}{2}))b-\frac{65}{28} & \text{Neem samen} \\ &=-b^2-\frac{96}{14}b-\frac{65}{28} & \text{Maak de som} \\ &=-b^2-\frac{48}{7}b-\frac{65}{28} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(x-(-4))(q-\frac{-4}{8})& =(\color{red}{x}+\color{orange}{4}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{2}x+4q+4.\frac{1}{2}& \text{Uitwerken } \\ & =qx+\frac{1}{2}x+4q+\frac{4}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{2}x+4q+2 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-10}{13})(\frac{3}{7}-x)& =(\color{red}{p}+\color{orange}{\frac{10}{13}}).(\color{green}{-x}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{10}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{3}{7}p-\frac{10}{13}x+\frac{10}{13}.\frac{3}{7}& \text{Uitwerken } \\ & =-px+\frac{3}{7}p-\frac{10}{13}x+\frac{30}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-12}{11})(q-\frac{-18}{13})& =(\color{red}{a}+\color{orange}{\frac{-12}{11}}).(\color{green}{q}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{18}{13}a-\frac{12}{11}q-\frac{12}{11}.\frac{18}{13}& \text{Uitwerken } \\ & =aq+\frac{18}{13}a-\frac{12}{11}q-\frac{216}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{14}{5})(a+\frac{-18}{8})& =(\color{red}{b}+\color{orange}{\frac{-14}{5}}).(\color{green}{a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{4}b-\frac{14}{5}a+\frac{14}{5}.\frac{9}{4}& \text{Uitwerken } \\ & =ab-\frac{9}{4}b-\frac{14}{5}a+\frac{126}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{9}{4}b-\frac{14}{5}a+\frac{63}{10} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x+\frac{14}{12})(x+\frac{11}{7})& =(\color{red}{x}+\color{orange}{\frac{7}{6}}).(\color{green}{x}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(\frac{7}{6})} . \color{green}{(x)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{11}{7}x+\frac{7}{6}x+\frac{7}{6}.\frac{11}{7}& \text{Uitwerken } \\ & =x^2+(\frac{11}{7}+\frac{7}{6})x+\frac{77}{42} & \text{Neem samen} \\ &=x^2+\frac{115}{42}x+\frac{77}{42} & \text{Maak de som} \\ &=x^2+\frac{115}{42}x+\frac{11}{6} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(b+\frac{7}{15})(q-\frac{19}{7})& =(\color{red}{b}+\color{orange}{\frac{7}{15}}).(\color{green}{q}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{7}{15})} . \color{green}{(q)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{7}b+\frac{7}{15}q-\frac{7}{15}.\frac{19}{7}& \text{Uitwerken } \\ & =bq-\frac{19}{7}b+\frac{7}{15}q-\frac{133}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{19}{7}b+\frac{7}{15}q-\frac{19}{15} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-7}{20})(b+\frac{5}{13})& =(\color{red}{b}+\color{orange}{\frac{-7}{20}}).(\color{green}{b}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{13}b-\frac{7}{20}b-\frac{7}{20}.\frac{5}{13}& \text{Uitwerken } \\ & =b^2+(\frac{5}{13}+(\frac{-7}{20}))b-(\frac{-35}{260}) & \text{Neem samen} \\ &=b^2+\frac{9}{260}b-(\frac{-35}{260}) & \text{Maak de som} \\ &=b^2+\frac{9}{260}b+\frac{7}{52} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(x+\frac{10}{18})(\frac{19}{14}+a)& =(\color{red}{x}+\color{orange}{\frac{5}{9}}).(\color{green}{a}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{14}x+\frac{5}{9}a+\frac{5}{9}.\frac{19}{14}& \text{Uitwerken } \\ & =ax+\frac{19}{14}x+\frac{5}{9}a+\frac{95}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{4}+p)(q+5)& =(\color{red}{p}+\color{orange}{\frac{13}{4}}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(5)} + \color{orange}{(\frac{13}{4})} . \color{green}{(q)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = pq+5p+\frac{13}{4}q+\frac{13}{4}.5& \text{Uitwerken } \\ & =pq+5p+\frac{13}{4}q+\frac{65}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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