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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{5}-a)(b-\frac{-8}{15})& =(\color{red}{-a}+\color{orange}{\frac{-19}{5}}).(\color{green}{b}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{8}{15}a-\frac{19}{5}b-\frac{19}{5}.\frac{8}{15}& \text{Uitwerken } \\ & =-ab-\frac{8}{15}a-\frac{19}{5}b-\frac{152}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(3-b)(b+\frac{-16}{8})& =(\color{red}{-b}+\color{orange}{3}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(-2)} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bb+2b+3b-3.2& \text{Uitwerken } \\ & =-b^2+(2+3)b-6 & \text{Neem samen} \\ &=-b^2+5b-6 & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-4}{5})(\frac{-16}{7}+p)& =(\color{red}{q}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{-16}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{7})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-16}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{16}{7}q+\frac{4}{5}p-\frac{4}{5}.\frac{16}{7}& \text{Uitwerken } \\ & =pq-\frac{16}{7}q+\frac{4}{5}p-\frac{64}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{20}{3})(a-\frac{13}{10})& =(\color{red}{p}+\color{orange}{\frac{-20}{3}}).(\color{green}{a}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{10}p-\frac{20}{3}a+\frac{20}{3}.\frac{13}{10}& \text{Uitwerken } \\ & =ap-\frac{13}{10}p-\frac{20}{3}a+\frac{260}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{13}{10}p-\frac{20}{3}a+\frac{26}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x-\frac{-5}{12})(\frac{-4}{11}-b)& =(\color{red}{x}+\color{orange}{\frac{5}{12}}).(\color{green}{-b}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{5}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{11}x-\frac{5}{12}b-\frac{5}{12}.\frac{4}{11}& \text{Uitwerken } \\ & =-bx-\frac{4}{11}x-\frac{5}{12}b-\frac{20}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{4}{11}x-\frac{5}{12}b-\frac{5}{33} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-15}{10}+p)(\frac{1}{11}+q)& =(\color{red}{p}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{11}p-\frac{3}{2}q-\frac{3}{2}.\frac{1}{11}& \text{Uitwerken } \\ & =pq+\frac{1}{11}p-\frac{3}{2}q-\frac{3}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-20}{17}+b)(b-\frac{16}{16})& =(\color{red}{b}+\color{orange}{\frac{-20}{17}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-20}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bb-1b-\frac{20}{17}b+\frac{20}{17}.1& \text{Uitwerken } \\ & =b^2+((-1)+(\frac{-20}{17}))b+\frac{20}{17} & \text{Neem samen} \\ &=b^2-\frac{37}{17}b+\frac{20}{17} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-16}{5})(\frac{-14}{11}+p)& =(\color{red}{q}+\color{orange}{\frac{-16}{5}}).(\color{green}{p}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{14}{11}q-\frac{16}{5}p+\frac{16}{5}.\frac{14}{11}& \text{Uitwerken } \\ & =pq-\frac{14}{11}q-\frac{16}{5}p+\frac{224}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{11}{9})(\frac{6}{9}-b)& =(\color{red}{b}+\color{orange}{\frac{-11}{9}}).(\color{green}{-b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{2}{3}b+\frac{11}{9}b-\frac{11}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =-b^2+(\frac{2}{3}+\frac{11}{9})b-\frac{22}{27} & \text{Neem samen} \\ &=-b^2+\frac{17}{9}b-\frac{22}{27} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(x+\frac{4}{19})(a-\frac{-17}{18})& =(\color{red}{x}+\color{orange}{\frac{4}{19}}).(\color{green}{a}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{4}{19})} . \color{green}{(a)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{18}x+\frac{4}{19}a+\frac{4}{19}.\frac{17}{18}& \text{Uitwerken } \\ & =ax+\frac{17}{18}x+\frac{4}{19}a+\frac{68}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{17}{18}x+\frac{4}{19}a+\frac{34}{171} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{6}{13}+q)(\frac{12}{4}+b)& =(\color{red}{q}+\color{orange}{\frac{6}{13}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{6}{13})} . \color{green}{(b)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bq+3q+\frac{6}{13}b+\frac{6}{13}.3& \text{Uitwerken } \\ & =bq+3q+\frac{6}{13}b+\frac{18}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-14}{16})(a-\frac{8}{2})& =(\color{red}{a}+\color{orange}{\frac{7}{8}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aa-4a+\frac{7}{8}a-\frac{7}{8}.4& \text{Uitwerken } \\ & =a^2+((-4)+\frac{7}{8})a-(\frac{-28}{8}) & \text{Neem samen} \\ &=a^2-\frac{25}{8}a-(\frac{-28}{8}) & \text{Maak de som} \\ &=a^2-\frac{25}{8}a+\frac{7}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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