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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{4}{10})(\frac{-20}{13}-p)& =(\color{red}{q}+\color{orange}{\frac{2}{5}}).(\color{green}{-p}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{20}{13}q-\frac{2}{5}p-\frac{2}{5}.\frac{20}{13}& \text{Uitwerken } \\ & =-pq-\frac{20}{13}q-\frac{2}{5}p-\frac{40}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{20}{13}q-\frac{2}{5}p-\frac{8}{13} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{11}-b)(p-\frac{-8}{10})& =(\color{red}{-b}+\color{orange}{\frac{-12}{11}}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{5}b-\frac{12}{11}p-\frac{12}{11}.\frac{4}{5}& \text{Uitwerken } \\ & =-bp-\frac{4}{5}b-\frac{12}{11}p-\frac{48}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-7}{19}-p)(q+\frac{-7}{12})& =(\color{red}{-p}+\color{orange}{\frac{-7}{19}}).(\color{green}{q}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{-7}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{19})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{7}{12}p-\frac{7}{19}q+\frac{7}{19}.\frac{7}{12}& \text{Uitwerken } \\ & =-pq+\frac{7}{12}p-\frac{7}{19}q+\frac{49}{228} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-18}{2})(\frac{2}{15}+x)& =(\color{red}{x}+\color{orange}{9}).(\color{green}{x}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(9)} . \color{green}{(x)} + \color{orange}{(9)} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{2}{15}x+9x+9.\frac{2}{15}& \text{Uitwerken } \\ & =x^2+(\frac{2}{15}+9)x+\frac{18}{15} & \text{Neem samen} \\ &=x^2+\frac{137}{15}x+\frac{18}{15} & \text{Maak de som} \\ &=x^2+\frac{137}{15}x+\frac{6}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-17}{5})(x-\frac{-10}{7})& =(\color{red}{a}+\color{orange}{\frac{17}{5}}).(\color{green}{x}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{17}{5})} . \color{green}{(x)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{10}{7}a+\frac{17}{5}x+\frac{17}{5}.\frac{10}{7}& \text{Uitwerken } \\ & =ax+\frac{10}{7}a+\frac{17}{5}x+\frac{170}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{10}{7}a+\frac{17}{5}x+\frac{34}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{8}{18}-a)(\frac{-18}{8}+b)& =(\color{red}{-a}+\color{orange}{\frac{4}{9}}).(\color{green}{b}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{9}{4}a+\frac{4}{9}b-\frac{4}{9}.\frac{9}{4}& \text{Uitwerken } \\ & =-ab+\frac{9}{4}a+\frac{4}{9}b-\frac{36}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{9}{4}a+\frac{4}{9}b-1 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{20}{6}+p)(p-\frac{-11}{11})& =(\color{red}{p}+\color{orange}{\frac{10}{3}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pp+1p+\frac{10}{3}p+\frac{10}{3}.1& \text{Uitwerken } \\ & =p^2+(1+\frac{10}{3})p+\frac{10}{3} & \text{Neem samen} \\ &=p^2+\frac{13}{3}p+\frac{10}{3} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(x-\frac{14}{5})(x-\frac{17}{20})& =(\color{red}{x}+\color{orange}{\frac{-14}{5}}).(\color{green}{x}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{17}{20}x-\frac{14}{5}x+\frac{14}{5}.\frac{17}{20}& \text{Uitwerken } \\ & =x^2+((\frac{-17}{20})+(\frac{-14}{5}))x+\frac{238}{100} & \text{Neem samen} \\ &=x^2-\frac{73}{20}x+\frac{238}{100} & \text{Maak de som} \\ &=x^2-\frac{73}{20}x+\frac{119}{50} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(a-\frac{18}{12})(19+q)& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{19})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(19)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = aq+19a-\frac{3}{2}q-\frac{3}{2}.19& \text{Uitwerken } \\ & =aq+19a-\frac{3}{2}q-\frac{57}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-19}{11}-b)(q+\frac{20}{13})& =(\color{red}{-b}+\color{orange}{\frac{-19}{11}}).(\color{green}{q}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{20}{13}b-\frac{19}{11}q-\frac{19}{11}.\frac{20}{13}& \text{Uitwerken } \\ & =-bq-\frac{20}{13}b-\frac{19}{11}q-\frac{380}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{11}{8}-x)(\frac{19}{7}+q)& =(\color{red}{-x}+\color{orange}{\frac{11}{8}}).(\color{green}{q}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(\frac{11}{8})} . \color{green}{(q)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{7}x+\frac{11}{8}q+\frac{11}{8}.\frac{19}{7}& \text{Uitwerken } \\ & =-qx-\frac{19}{7}x+\frac{11}{8}q+\frac{209}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{13}{13})(x+\frac{-11}{6})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{6}p-1x+1.\frac{11}{6}& \text{Uitwerken } \\ & =px-\frac{11}{6}p-1x+\frac{11}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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