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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{8}{9})(\frac{16}{12}+b)& =(\color{red}{p}+\color{orange}{\frac{8}{9}}).(\color{green}{b}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{8}{9})} . \color{green}{(b)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{3}p+\frac{8}{9}b+\frac{8}{9}.\frac{4}{3}& \text{Uitwerken } \\ & =bp+\frac{4}{3}p+\frac{8}{9}b+\frac{32}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{2}{13}-b)(\frac{12}{10}+a)& =(\color{red}{-b}+\color{orange}{\frac{2}{13}}).(\color{green}{a}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{2}{13})} . \color{green}{(a)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{6}{5}b+\frac{2}{13}a+\frac{2}{13}.\frac{6}{5}& \text{Uitwerken } \\ & =-ab-\frac{6}{5}b+\frac{2}{13}a+\frac{12}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-9}{19}+p)(p-\frac{13}{13})& =(\color{red}{p}+\color{orange}{\frac{-9}{19}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-9}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pp-1p-\frac{9}{19}p+\frac{9}{19}.1& \text{Uitwerken } \\ & =p^2+((-1)+(\frac{-9}{19}))p+\frac{9}{19} & \text{Neem samen} \\ &=p^2-\frac{28}{19}p+\frac{9}{19} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(q+\frac{2}{8})(a+\frac{-9}{2})& =(\color{red}{q}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{9}{2}q+\frac{1}{4}a-\frac{1}{4}.\frac{9}{2}& \text{Uitwerken } \\ & =aq-\frac{9}{2}q+\frac{1}{4}a-\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{13}+q)(b+\frac{-6}{8})& =(\color{red}{q}+\color{orange}{\frac{10}{13}}).(\color{green}{b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{10}{13})} . \color{green}{(b)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{4}q+\frac{10}{13}b-\frac{10}{13}.\frac{3}{4}& \text{Uitwerken } \\ & =bq-\frac{3}{4}q+\frac{10}{13}b-\frac{30}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{3}{4}q+\frac{10}{13}b-\frac{15}{26} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-19}{19}+q)(\frac{-1}{13}-q)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{13}q+1q+1.\frac{1}{13}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{13})+1)q+(\frac{-1}{13}) & \text{Neem samen} \\ &=-q^2+\frac{12}{13}q+(\frac{-1}{13}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-15}{7})(p+\frac{-6}{5})& =(\color{red}{b}+\color{orange}{\frac{-15}{7}}).(\color{green}{p}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{5}b-\frac{15}{7}p+\frac{15}{7}.\frac{6}{5}& \text{Uitwerken } \\ & =bp-\frac{6}{5}b-\frac{15}{7}p+\frac{90}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{6}{5}b-\frac{15}{7}p+\frac{18}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a+\frac{9}{13})(\frac{-6}{4}+q)& =(\color{red}{a}+\color{orange}{\frac{9}{13}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{9}{13})} . \color{green}{(q)} + \color{orange}{(\frac{9}{13})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{2}a+\frac{9}{13}q-\frac{9}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =aq-\frac{3}{2}a+\frac{9}{13}q-\frac{27}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{19}{12})(\frac{9}{14}-x)& =(\color{red}{a}+\color{orange}{\frac{-19}{12}}).(\color{green}{-x}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{14}a+\frac{19}{12}x-\frac{19}{12}.\frac{9}{14}& \text{Uitwerken } \\ & =-ax+\frac{9}{14}a+\frac{19}{12}x-\frac{171}{168} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{9}{14}a+\frac{19}{12}x-\frac{57}{56} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{10}{12}+a)(p+\frac{-1}{8})& =(\color{red}{a}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{8}a+\frac{5}{6}p-\frac{5}{6}.\frac{1}{8}& \text{Uitwerken } \\ & =ap-\frac{1}{8}a+\frac{5}{6}p-\frac{5}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-17}{11})(\frac{7}{11}-b)& =(\color{red}{x}+\color{orange}{\frac{17}{11}}).(\color{green}{-b}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{17}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{11}x-\frac{17}{11}b+\frac{17}{11}.\frac{7}{11}& \text{Uitwerken } \\ & =-bx+\frac{7}{11}x-\frac{17}{11}b+\frac{119}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-6}{15})(\frac{15}{4}-q)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{-q}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{15}{4}x+\frac{2}{5}q-\frac{2}{5}.\frac{15}{4}& \text{Uitwerken } \\ & =-qx+\frac{15}{4}x+\frac{2}{5}q-\frac{30}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{15}{4}x+\frac{2}{5}q-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
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