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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{10}-p)(\frac{-10}{5}-p)& =(\color{red}{-p}+\color{orange}{\frac{11}{10}}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(\frac{11}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pp+2p-\frac{11}{10}p-\frac{11}{10}.2& \text{Uitwerken } \\ & =p^2+(2+(\frac{-11}{10}))p-(\frac{-22}{10}) & \text{Neem samen} \\ &=p^2+\frac{9}{10}p-(\frac{-22}{10}) & \text{Maak de som} \\ &=p^2+\frac{9}{10}p+\frac{11}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(p+(-17))(b+\frac{18}{14})& =(\color{red}{p}+\color{orange}{(-17)}).(\color{green}{b}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(-17)} . \color{green}{(b)} + \color{orange}{(-17)} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{7}p-17b-17.\frac{9}{7}& \text{Uitwerken } \\ & =bp+\frac{9}{7}p-17b-\frac{153}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{12}{18}+q)(\frac{16}{13}+a)& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{16}{13}q+\frac{2}{3}a+\frac{2}{3}.\frac{16}{13}& \text{Uitwerken } \\ & =aq+\frac{16}{13}q+\frac{2}{3}a+\frac{32}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-3}{6}-q)(a-2)& =(\color{red}{-q}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -aq+2q-\frac{1}{2}a+\frac{1}{2}.2& \text{Uitwerken } \\ & =-aq+2q-\frac{1}{2}a+\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+2q-\frac{1}{2}a+1 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-19}{9})(a+\frac{15}{18})& =(\color{red}{b}+\color{orange}{\frac{19}{9}}).(\color{green}{a}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{19}{9})} . \color{green}{(a)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{6}b+\frac{19}{9}a+\frac{19}{9}.\frac{5}{6}& \text{Uitwerken } \\ & =ab+\frac{5}{6}b+\frac{19}{9}a+\frac{95}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{15}{6})(\frac{-11}{12}-p)& =(\color{red}{p}+\color{orange}{\frac{5}{2}}).(\color{green}{-p}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{11}{12}p-\frac{5}{2}p-\frac{5}{2}.\frac{11}{12}& \text{Uitwerken } \\ & =-p^2+((\frac{-11}{12})+(\frac{-5}{2}))p-\frac{55}{24} & \text{Neem samen} \\ &=-p^2-\frac{41}{12}p-\frac{55}{24} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{12}{6}-x)(b+\frac{20}{14})& =(\color{red}{-x}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{10}{7}x+2b+2.\frac{10}{7}& \text{Uitwerken } \\ & =-bx-\frac{10}{7}x+2b+\frac{20}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-14}{9})(a-\frac{16}{9})& =(\color{red}{b}+\color{orange}{\frac{-14}{9}}).(\color{green}{a}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{16}{9}b-\frac{14}{9}a+\frac{14}{9}.\frac{16}{9}& \text{Uitwerken } \\ & =ab-\frac{16}{9}b-\frac{14}{9}a+\frac{224}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-19}{6})(\frac{8}{6}-a)& =(\color{red}{a}+\color{orange}{\frac{-19}{6}}).(\color{green}{-a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{4}{3}a+\frac{19}{6}a-\frac{19}{6}.\frac{4}{3}& \text{Uitwerken } \\ & =-a^2+(\frac{4}{3}+\frac{19}{6})a-\frac{76}{18} & \text{Neem samen} \\ &=-a^2+\frac{27}{6}a-\frac{76}{18} & \text{Maak de som} \\ &=-a^2+\frac{9}{2}a-\frac{38}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(q+(-19))(\frac{4}{19}-x)& =(\color{red}{q}+\color{orange}{(-19)}).(\color{green}{-x}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(-19)} . \color{green}{(-x)} + \color{orange}{(-19)} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{4}{19}q+19x-19.\frac{4}{19}& \text{Uitwerken } \\ & =-qx+\frac{4}{19}q+19x-\frac{76}{19} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{4}{19}q+19x-4 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}((-2)+p)(\frac{-9}{2}-p)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{9}{2}p+2p+2.\frac{9}{2}& \text{Uitwerken } \\ & =-p^2+((\frac{-9}{2})+2)p+(\frac{-18}{2}) & \text{Neem samen} \\ &=-p^2-\frac{5}{2}p+(\frac{-18}{2}) & \text{Maak de som} \\ &=-p^2-\frac{5}{2}p+(-9) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-18}{3})(a+\frac{4}{5})& =(\color{red}{x}+\color{orange}{6}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(6)} . \color{green}{(a)} + \color{orange}{(6)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{5}x+6a+6.\frac{4}{5}& \text{Uitwerken } \\ & =ax+\frac{4}{5}x+6a+\frac{24}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-04-20 05:22:38