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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-2}{5})(a+\frac{8}{8})& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1x+\frac{2}{5}a+\frac{2}{5}.1& \text{Uitwerken } \\ & =ax+1x+\frac{2}{5}a+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-1}{10}+p)(\frac{-10}{17}+p)& =(\color{red}{p}+\color{orange}{\frac{-1}{10}}).(\color{green}{p}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{10}{17}p-\frac{1}{10}p+\frac{1}{10}.\frac{10}{17}& \text{Uitwerken } \\ & =p^2+((\frac{-10}{17})+(\frac{-1}{10}))p+\frac{10}{170} & \text{Neem samen} \\ &=p^2-\frac{117}{170}p+\frac{10}{170} & \text{Maak de som} \\ &=p^2-\frac{117}{170}p+\frac{1}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(a+\frac{2}{6})(\frac{-17}{15}-p)& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{-p}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{15}a-\frac{1}{3}p-\frac{1}{3}.\frac{17}{15}& \text{Uitwerken } \\ & =-ap-\frac{17}{15}a-\frac{1}{3}p-\frac{17}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{13}{9}-p)(b+\frac{-4}{20})& =(\color{red}{-p}+\color{orange}{\frac{13}{9}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{13}{9})} . \color{green}{(b)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{5}p+\frac{13}{9}b-\frac{13}{9}.\frac{1}{5}& \text{Uitwerken } \\ & =-bp+\frac{1}{5}p+\frac{13}{9}b-\frac{13}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{14}+p)(\frac{-3}{3}-p)& =(\color{red}{p}+\color{orange}{\frac{9}{14}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{9}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pp-1p-\frac{9}{14}p-\frac{9}{14}.1& \text{Uitwerken } \\ & =-p^2+((-1)+(\frac{-9}{14}))p-\frac{9}{14} & \text{Neem samen} \\ &=-p^2-\frac{23}{14}p-\frac{9}{14} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-11}{4})(\frac{-15}{17}+b)& =(\color{red}{q}+\color{orange}{\frac{11}{4}}).(\color{green}{b}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{11}{4})} . \color{green}{(b)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{15}{17}q+\frac{11}{4}b-\frac{11}{4}.\frac{15}{17}& \text{Uitwerken } \\ & =bq-\frac{15}{17}q+\frac{11}{4}b-\frac{165}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-4}{10}+p)(\frac{-1}{11}+p)& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{11}p-\frac{2}{5}p+\frac{2}{5}.\frac{1}{11}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{11})+(\frac{-2}{5}))p+\frac{2}{55} & \text{Neem samen} \\ &=p^2-\frac{27}{55}p+\frac{2}{55} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-17}{14})(p+\frac{-13}{19})& =(\color{red}{a}+\color{orange}{\frac{17}{14}}).(\color{green}{p}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{17}{14})} . \color{green}{(p)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{19}a+\frac{17}{14}p-\frac{17}{14}.\frac{13}{19}& \text{Uitwerken } \\ & =ap-\frac{13}{19}a+\frac{17}{14}p-\frac{221}{266} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{6}{18})(p+\frac{11}{11})& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1b-\frac{1}{3}p-\frac{1}{3}.1& \text{Uitwerken } \\ & =bp+1b-\frac{1}{3}p-\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{8}{11}+q)(\frac{-19}{7}-q)& =(\color{red}{q}+\color{orange}{\frac{8}{11}}).(\color{green}{-q}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{8}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{19}{7}q-\frac{8}{11}q-\frac{8}{11}.\frac{19}{7}& \text{Uitwerken } \\ & =-q^2+((\frac{-19}{7})+(\frac{-8}{11}))q-\frac{152}{77} & \text{Neem samen} \\ &=-q^2-\frac{265}{77}q-\frac{152}{77} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-13}{7})(a-\frac{6}{14})& =(\color{red}{a}+\color{orange}{\frac{13}{7}}).(\color{green}{a}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{13}{7})} . \color{green}{(a)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{7}a+\frac{13}{7}a-\frac{13}{7}.\frac{3}{7}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{7})+\frac{13}{7})a-(\frac{-39}{49}) & \text{Neem samen} \\ &=a^2+\frac{10}{7}a-(\frac{-39}{49}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-11}{15})(\frac{4}{11}+a)& =(\color{red}{a}+\color{orange}{\frac{11}{15}}).(\color{green}{a}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{11}{15})} . \color{green}{(a)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{4}{11}a+\frac{11}{15}a+\frac{11}{15}.\frac{4}{11}& \text{Uitwerken } \\ & =a^2+(\frac{4}{11}+\frac{11}{15})a+\frac{44}{165} & \text{Neem samen} \\ &=a^2+\frac{181}{165}a+\frac{44}{165} & \text{Maak de som} \\ &=a^2+\frac{181}{165}a+\frac{4}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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