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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-7}{6}+a)(\frac{-19}{16}+p)& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{p}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{16}a-\frac{7}{6}p+\frac{7}{6}.\frac{19}{16}& \text{Uitwerken } \\ & =ap-\frac{19}{16}a-\frac{7}{6}p+\frac{133}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-3}{4}+q)(\frac{-2}{5}-b)& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{-b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{2}{5}q+\frac{3}{4}b+\frac{3}{4}.\frac{2}{5}& \text{Uitwerken } \\ & =-bq-\frac{2}{5}q+\frac{3}{4}b+\frac{6}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{2}{5}q+\frac{3}{4}b+\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-12}{4}+q)(p-\frac{-8}{6})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{3}q-3p-3.\frac{4}{3}& \text{Uitwerken } \\ & =pq+\frac{4}{3}q-3p-\frac{12}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{4}{3}q-3p-4 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{4}{11})(x+3)& =(\color{red}{p}+\color{orange}{\frac{-4}{11}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{-4}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = px+3p-\frac{4}{11}x-\frac{4}{11}.3& \text{Uitwerken } \\ & =px+3p-\frac{4}{11}x-\frac{12}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-13}{14})(\frac{-9}{9}+q)& =(\color{red}{a}+\color{orange}{\frac{-13}{14}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-13}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a-\frac{13}{14}q+\frac{13}{14}.1& \text{Uitwerken } \\ & =aq-1a-\frac{13}{14}q+\frac{13}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-16}{15}+a)(q+\frac{-2}{20})& =(\color{red}{a}+\color{orange}{\frac{-16}{15}}).(\color{green}{q}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{10}a-\frac{16}{15}q+\frac{16}{15}.\frac{1}{10}& \text{Uitwerken } \\ & =aq-\frac{1}{10}a-\frac{16}{15}q+\frac{16}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{10}a-\frac{16}{15}q+\frac{8}{75} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{19}{8}+b)(b+\frac{-9}{8})& =(\color{red}{b}+\color{orange}{\frac{19}{8}}).(\color{green}{b}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{19}{8})} . \color{green}{(b)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{9}{8}b+\frac{19}{8}b-\frac{19}{8}.\frac{9}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-9}{8})+\frac{19}{8})b-(\frac{-171}{64}) & \text{Neem samen} \\ &=b^2+\frac{10}{8}b-(\frac{-171}{64}) & \text{Maak de som} \\ &=b^2+\frac{5}{4}b+\frac{171}{64} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}((-8)+p)(b-\frac{-6}{2})& =(\color{red}{p}+\color{orange}{(-8)}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(-8)} . \color{green}{(b)} + \color{orange}{(-8)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bp+3p-8b-8.3& \text{Uitwerken } \\ & =bp+3p-8b-24 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-16}{6})(a+\frac{6}{20})& =(\color{red}{p}+\color{orange}{\frac{8}{3}}).(\color{green}{a}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{8}{3})} . \color{green}{(a)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{10}p+\frac{8}{3}a+\frac{8}{3}.\frac{3}{10}& \text{Uitwerken } \\ & =ap+\frac{3}{10}p+\frac{8}{3}a+\frac{24}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{10}p+\frac{8}{3}a+\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{19}{7}-q)(\frac{-16}{11}-x)& =(\color{red}{-q}+\color{orange}{\frac{19}{7}}).(\color{green}{-x}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{19}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{16}{11}q-\frac{19}{7}x-\frac{19}{7}.\frac{16}{11}& \text{Uitwerken } \\ & =qx+\frac{16}{11}q-\frac{19}{7}x-\frac{304}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{1}{3}+a)(\frac{-18}{13}+a)& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{a}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{18}{13}a+\frac{1}{3}a-\frac{1}{3}.\frac{18}{13}& \text{Uitwerken } \\ & =a^2+((\frac{-18}{13})+\frac{1}{3})a-(\frac{-18}{39}) & \text{Neem samen} \\ &=a^2-\frac{41}{39}a-(\frac{-18}{39}) & \text{Maak de som} \\ &=a^2-\frac{41}{39}a+\frac{6}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{-16}{15}+p)(\frac{19}{3}-p)& =(\color{red}{p}+\color{orange}{\frac{-16}{15}}).(\color{green}{-p}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{19}{3}p+\frac{16}{15}p-\frac{16}{15}.\frac{19}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{19}{3}+\frac{16}{15})p-\frac{304}{45} & \text{Neem samen} \\ &=-p^2+\frac{111}{15}p-\frac{304}{45} & \text{Maak de som} \\ &=-p^2+\frac{37}{5}p-\frac{304}{45} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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