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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-8}{15}-b)(\frac{-7}{9}+x)& =(\color{red}{-b}+\color{orange}{\frac{-8}{15}}).(\color{green}{x}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{9}b-\frac{8}{15}x+\frac{8}{15}.\frac{7}{9}& \text{Uitwerken } \\ & =-bx+\frac{7}{9}b-\frac{8}{15}x+\frac{56}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-16}{20})(p-\frac{-8}{5})& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{8}{5}b+\frac{4}{5}p+\frac{4}{5}.\frac{8}{5}& \text{Uitwerken } \\ & =bp+\frac{8}{5}b+\frac{4}{5}p+\frac{32}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{4}{10})(\frac{-17}{8}+p)& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{p}+\color{blue}{\frac{-17}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{8})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-17}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{8}p-\frac{2}{5}p+\frac{2}{5}.\frac{17}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{8})+(\frac{-2}{5}))p+\frac{34}{40} & \text{Neem samen} \\ &=p^2-\frac{101}{40}p+\frac{34}{40} & \text{Maak de som} \\ &=p^2-\frac{101}{40}p+\frac{17}{20} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-9}{11})(a-\frac{5}{5})& =(\color{red}{b}+\color{orange}{\frac{-9}{11}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-9}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1b-\frac{9}{11}a+\frac{9}{11}.1& \text{Uitwerken } \\ & =ab-1b-\frac{9}{11}a+\frac{9}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{1}{7}-p)(\frac{6}{15}+q)& =(\color{red}{-p}+\color{orange}{\frac{1}{7}}).(\color{green}{q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{5}p+\frac{1}{7}q+\frac{1}{7}.\frac{2}{5}& \text{Uitwerken } \\ & =-pq-\frac{2}{5}p+\frac{1}{7}q+\frac{2}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{15}{13}-x)(\frac{4}{7}-q)& =(\color{red}{-x}+\color{orange}{\frac{15}{13}}).(\color{green}{-q}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{15}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{7}x-\frac{15}{13}q+\frac{15}{13}.\frac{4}{7}& \text{Uitwerken } \\ & =qx-\frac{4}{7}x-\frac{15}{13}q+\frac{60}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-12)(b+\frac{16}{10})& =(\color{red}{x}+\color{orange}{(-12)}).(\color{green}{b}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(-12)} . \color{green}{(b)} + \color{orange}{(-12)} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{8}{5}x-12b-12.\frac{8}{5}& \text{Uitwerken } \\ & =bx+\frac{8}{5}x-12b-\frac{96}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{20}+p)(\frac{-3}{14}-a)& =(\color{red}{p}+\color{orange}{\frac{1}{5}}).(\color{green}{-a}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{14}p-\frac{1}{5}a-\frac{1}{5}.\frac{3}{14}& \text{Uitwerken } \\ & =-ap-\frac{3}{14}p-\frac{1}{5}a-\frac{3}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{20}{14}+a)(q-\frac{-9}{17})& =(\color{red}{a}+\color{orange}{\frac{10}{7}}).(\color{green}{q}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{10}{7})} . \color{green}{(q)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{17}a+\frac{10}{7}q+\frac{10}{7}.\frac{9}{17}& \text{Uitwerken } \\ & =aq+\frac{9}{17}a+\frac{10}{7}q+\frac{90}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{4}{7})(7-q)& =(\color{red}{a}+\color{orange}{\frac{-4}{7}}).(\color{green}{-q}+\color{blue}{7})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(7)} + \color{orange}{(\frac{-4}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = -aq+7a+\frac{4}{7}q-\frac{4}{7}.7& \text{Uitwerken } \\ & =-aq+7a+\frac{4}{7}q-\frac{28}{7} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+7a+\frac{4}{7}q-4 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b-\frac{8}{9})(\frac{-17}{13}+p)& =(\color{red}{b}+\color{orange}{\frac{-8}{9}}).(\color{green}{p}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{17}{13}b-\frac{8}{9}p+\frac{8}{9}.\frac{17}{13}& \text{Uitwerken } \\ & =bp-\frac{17}{13}b-\frac{8}{9}p+\frac{136}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{5}{9}-q)(b-\frac{-9}{11})& =(\color{red}{-q}+\color{orange}{\frac{5}{9}}).(\color{green}{b}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{5}{9})} . \color{green}{(b)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{11}q+\frac{5}{9}b+\frac{5}{9}.\frac{9}{11}& \text{Uitwerken } \\ & =-bq-\frac{9}{11}q+\frac{5}{9}b+\frac{45}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{9}{11}q+\frac{5}{9}b+\frac{5}{11} & \text{Vereenvoudig} \\\end{align}\)
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