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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{17}{5})(\frac{-6}{11}+a)& =(\color{red}{p}+\color{orange}{\frac{17}{5}}).(\color{green}{a}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{17}{5})} . \color{green}{(a)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{6}{11}p+\frac{17}{5}a-\frac{17}{5}.\frac{6}{11}& \text{Uitwerken } \\ & =ap-\frac{6}{11}p+\frac{17}{5}a-\frac{102}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-11}{8})(\frac{-2}{3}+q)& =(\color{red}{p}+\color{orange}{\frac{-11}{8}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{3}p-\frac{11}{8}q+\frac{11}{8}.\frac{2}{3}& \text{Uitwerken } \\ & =pq-\frac{2}{3}p-\frac{11}{8}q+\frac{22}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{2}{3}p-\frac{11}{8}q+\frac{11}{12} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{11}{17}+a)(x-\frac{-10}{7})& =(\color{red}{a}+\color{orange}{\frac{11}{17}}).(\color{green}{x}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{11}{17})} . \color{green}{(x)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{10}{7}a+\frac{11}{17}x+\frac{11}{17}.\frac{10}{7}& \text{Uitwerken } \\ & =ax+\frac{10}{7}a+\frac{11}{17}x+\frac{110}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-15)(\frac{-4}{19}+q)& =(\color{red}{b}+\color{orange}{(-15)}).(\color{green}{q}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(-15)} . \color{green}{(q)} + \color{orange}{(-15)} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{19}b-15q+15.\frac{4}{19}& \text{Uitwerken } \\ & =bq-\frac{4}{19}b-15q+\frac{60}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{15}+q)(p-\frac{-1}{4})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{4}q+\frac{2}{3}p+\frac{2}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =pq+\frac{1}{4}q+\frac{2}{3}p+\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{4}q+\frac{2}{3}p+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{15}{3}-q)(x+\frac{-7}{11})& =(\color{red}{-q}+\color{orange}{5}).(\color{green}{x}+\color{blue}{\frac{-7}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{11})} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(\frac{-7}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{7}{11}q+5x-5.\frac{7}{11}& \text{Uitwerken } \\ & =-qx+\frac{7}{11}q+5x-\frac{35}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-6}{4}-x)(x-\frac{16}{5})& =(\color{red}{-x}+\color{orange}{\frac{-3}{2}}).(\color{green}{x}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{16}{5}x-\frac{3}{2}x+\frac{3}{2}.\frac{16}{5}& \text{Uitwerken } \\ & =-x^2+(\frac{16}{5}+(\frac{-3}{2}))x+(\frac{-48}{10}) & \text{Neem samen} \\ &=-x^2+\frac{17}{10}x+(\frac{-48}{10}) & \text{Maak de som} \\ &=-x^2+\frac{17}{10}x+(\frac{-24}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(p+\frac{10}{2})(p+\frac{19}{13})& =(\color{red}{p}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{19}{13}p+5p+5.\frac{19}{13}& \text{Uitwerken } \\ & =p^2+(\frac{19}{13}+5)p+\frac{95}{13} & \text{Neem samen} \\ &=p^2+\frac{84}{13}p+\frac{95}{13} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-7}{16}-b)(\frac{8}{19}+x)& =(\color{red}{-b}+\color{orange}{\frac{-7}{16}}).(\color{green}{x}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{-7}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{8}{19}b-\frac{7}{16}x-\frac{7}{16}.\frac{8}{19}& \text{Uitwerken } \\ & =-bx-\frac{8}{19}b-\frac{7}{16}x-\frac{56}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{8}{19}b-\frac{7}{16}x-\frac{7}{38} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-2}{3})(a-\frac{-1}{3})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{3}b-\frac{2}{3}a-\frac{2}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =ab+\frac{1}{3}b-\frac{2}{3}a-\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-4}{9})(\frac{13}{11}+a)& =(\color{red}{x}+\color{orange}{\frac{4}{9}}).(\color{green}{a}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{13}{11}x+\frac{4}{9}a+\frac{4}{9}.\frac{13}{11}& \text{Uitwerken } \\ & =ax+\frac{13}{11}x+\frac{4}{9}a+\frac{52}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-\frac{6}{11})(\frac{-16}{6}+a)& =(\color{red}{q}+\color{orange}{\frac{-6}{11}}).(\color{green}{a}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{8}{3}q-\frac{6}{11}a+\frac{6}{11}.\frac{8}{3}& \text{Uitwerken } \\ & =aq-\frac{8}{3}q-\frac{6}{11}a+\frac{48}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{8}{3}q-\frac{6}{11}a+\frac{16}{11} & \text{Vereenvoudig} \\\end{align}\)
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