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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{16}{7})(\frac{-20}{11}-p)& =(\color{red}{p}+\color{orange}{\frac{-16}{7}}).(\color{green}{-p}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{20}{11}p+\frac{16}{7}p+\frac{16}{7}.\frac{20}{11}& \text{Uitwerken } \\ & =-p^2+((\frac{-20}{11})+\frac{16}{7})p+(\frac{-320}{77}) & \text{Neem samen} \\ &=-p^2+\frac{36}{77}p+(\frac{-320}{77}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-7}{4}+b)(\frac{-19}{15}+a)& =(\color{red}{b}+\color{orange}{\frac{-7}{4}}).(\color{green}{a}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{15}b-\frac{7}{4}a+\frac{7}{4}.\frac{19}{15}& \text{Uitwerken } \\ & =ab-\frac{19}{15}b-\frac{7}{4}a+\frac{133}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-5}{5})(\frac{-13}{10}+x)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{10}p-1x+1.\frac{13}{10}& \text{Uitwerken } \\ & =px-\frac{13}{10}p-1x+\frac{13}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{17}{14}+p)(\frac{-8}{5}+q)& =(\color{red}{p}+\color{orange}{\frac{17}{14}}).(\color{green}{q}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{17}{14})} . \color{green}{(q)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{5}p+\frac{17}{14}q-\frac{17}{14}.\frac{8}{5}& \text{Uitwerken } \\ & =pq-\frac{8}{5}p+\frac{17}{14}q-\frac{136}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{8}{5}p+\frac{17}{14}q-\frac{68}{35} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{17}{8})(a+\frac{9}{18})& =(\color{red}{a}+\color{orange}{\frac{-17}{8}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-17}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{2}a-\frac{17}{8}a-\frac{17}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =a^2+(\frac{1}{2}+(\frac{-17}{8}))a-(\frac{-17}{16}) & \text{Neem samen} \\ &=a^2-\frac{13}{8}a-(\frac{-17}{16}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{3}{17}+q)(q+\frac{-7}{13})& =(\color{red}{q}+\color{orange}{\frac{3}{17}}).(\color{green}{q}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{3}{17})} . \color{green}{(q)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{13}q+\frac{3}{17}q-\frac{3}{17}.\frac{7}{13}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{13})+\frac{3}{17})q-(\frac{-21}{221}) & \text{Neem samen} \\ &=q^2-\frac{80}{221}q-(\frac{-21}{221}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b+\frac{11}{18})(x+\frac{-15}{14})& =(\color{red}{b}+\color{orange}{\frac{11}{18}}).(\color{green}{x}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(\frac{11}{18})} . \color{green}{(x)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{15}{14}b+\frac{11}{18}x-\frac{11}{18}.\frac{15}{14}& \text{Uitwerken } \\ & =bx-\frac{15}{14}b+\frac{11}{18}x-\frac{165}{252} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{15}{14}b+\frac{11}{18}x-\frac{55}{84} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-1}{8}+x)((-3)-p)& =(\color{red}{x}+\color{orange}{\frac{-1}{8}}).(\color{green}{-p}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -px-3x+\frac{1}{8}p+\frac{1}{8}.3& \text{Uitwerken } \\ & =-px-3x+\frac{1}{8}p+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{10}-p)(\frac{5}{11}+a)& =(\color{red}{-p}+\color{orange}{\frac{2}{5}}).(\color{green}{a}+\color{blue}{\frac{5}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{11})} + \color{orange}{(\frac{2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{5}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{11}p+\frac{2}{5}a+\frac{2}{5}.\frac{5}{11}& \text{Uitwerken } \\ & =-ap-\frac{5}{11}p+\frac{2}{5}a+\frac{10}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{5}{11}p+\frac{2}{5}a+\frac{2}{11} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-13}{13})(\frac{-9}{18}-x)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{2}q+1x+1.\frac{1}{2}& \text{Uitwerken } \\ & =-qx-\frac{1}{2}q+1x+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-17}{9}-x)(\frac{-11}{6}-q)& =(\color{red}{-x}+\color{orange}{\frac{-17}{9}}).(\color{green}{-q}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{6}x+\frac{17}{9}q+\frac{17}{9}.\frac{11}{6}& \text{Uitwerken } \\ & =qx+\frac{11}{6}x+\frac{17}{9}q+\frac{187}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{3}+q)(\frac{-9}{5}+q)& =(\color{red}{q}+\color{orange}{\frac{-10}{3}}).(\color{green}{q}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{9}{5}q-\frac{10}{3}q+\frac{10}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =q^2+((\frac{-9}{5})+(\frac{-10}{3}))q+\frac{90}{15} & \text{Neem samen} \\ &=q^2-\frac{77}{15}q+\frac{90}{15} & \text{Maak de som} \\ &=q^2-\frac{77}{15}q+6 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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