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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{8}{11}+p)(\frac{5}{3}-a)& =(\color{red}{p}+\color{orange}{\frac{8}{11}}).(\color{green}{-a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{8}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{3}p-\frac{8}{11}a+\frac{8}{11}.\frac{5}{3}& \text{Uitwerken } \\ & =-ap+\frac{5}{3}p-\frac{8}{11}a+\frac{40}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{18}{7}-x)(\frac{-10}{18}-a)& =(\color{red}{-x}+\color{orange}{\frac{18}{7}}).(\color{green}{-a}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{18}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{9}x-\frac{18}{7}a-\frac{18}{7}.\frac{5}{9}& \text{Uitwerken } \\ & =ax+\frac{5}{9}x-\frac{18}{7}a-\frac{90}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{5}{9}x-\frac{18}{7}a-\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-2}{16})(\frac{-16}{17}+a)& =(\color{red}{a}+\color{orange}{\frac{-1}{8}}).(\color{green}{a}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{16}{17}a-\frac{1}{8}a+\frac{1}{8}.\frac{16}{17}& \text{Uitwerken } \\ & =a^2+((\frac{-16}{17})+(\frac{-1}{8}))a+\frac{16}{136} & \text{Neem samen} \\ &=a^2-\frac{145}{136}a+\frac{16}{136} & \text{Maak de som} \\ &=a^2-\frac{145}{136}a+\frac{2}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(q+\frac{11}{18})(a+\frac{5}{3})& =(\color{red}{q}+\color{orange}{\frac{11}{18}}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{11}{18})} . \color{green}{(a)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{3}q+\frac{11}{18}a+\frac{11}{18}.\frac{5}{3}& \text{Uitwerken } \\ & =aq+\frac{5}{3}q+\frac{11}{18}a+\frac{55}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{4}{19})(\frac{-16}{7}+b)& =(\color{red}{x}+\color{orange}{\frac{-4}{19}}).(\color{green}{b}+\color{blue}{\frac{-16}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{7})} + \color{orange}{(\frac{-4}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{19})} . \color{blue}{(\frac{-16}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{16}{7}x-\frac{4}{19}b+\frac{4}{19}.\frac{16}{7}& \text{Uitwerken } \\ & =bx-\frac{16}{7}x-\frac{4}{19}b+\frac{64}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{11}{13})(p+\frac{-10}{11})& =(\color{red}{a}+\color{orange}{\frac{11}{13}}).(\color{green}{p}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{11}{13})} . \color{green}{(p)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{10}{11}a+\frac{11}{13}p-\frac{11}{13}.\frac{10}{11}& \text{Uitwerken } \\ & =ap-\frac{10}{11}a+\frac{11}{13}p-\frac{110}{143} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{10}{11}a+\frac{11}{13}p-\frac{10}{13} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{10}+b)(x-\frac{-13}{20})& =(\color{red}{b}+\color{orange}{\frac{-7}{5}}).(\color{green}{x}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{13}{20}b-\frac{7}{5}x-\frac{7}{5}.\frac{13}{20}& \text{Uitwerken } \\ & =bx+\frac{13}{20}b-\frac{7}{5}x-\frac{91}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-14}{19}+a)(x-\frac{9}{15})& =(\color{red}{a}+\color{orange}{\frac{-14}{19}}).(\color{green}{x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{5}a-\frac{14}{19}x+\frac{14}{19}.\frac{3}{5}& \text{Uitwerken } \\ & =ax-\frac{3}{5}a-\frac{14}{19}x+\frac{42}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{18}{18}+q)(\frac{-13}{18}-q)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{13}{18}q-1q-1.\frac{13}{18}& \text{Uitwerken } \\ & =-q^2+((\frac{-13}{18})+(-1))q-\frac{13}{18} & \text{Neem samen} \\ &=-q^2-\frac{31}{18}q-\frac{13}{18} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{19}{12}-a)(p+\frac{15}{14})& =(\color{red}{-a}+\color{orange}{\frac{19}{12}}).(\color{green}{p}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{19}{12})} . \color{green}{(p)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{15}{14}a+\frac{19}{12}p+\frac{19}{12}.\frac{15}{14}& \text{Uitwerken } \\ & =-ap-\frac{15}{14}a+\frac{19}{12}p+\frac{285}{168} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{15}{14}a+\frac{19}{12}p+\frac{95}{56} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{8}{11}-q)(x-\frac{-18}{9})& =(\color{red}{-q}+\color{orange}{\frac{8}{11}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{8}{11})} . \color{green}{(x)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qx-2q+\frac{8}{11}x+\frac{8}{11}.2& \text{Uitwerken } \\ & =-qx-2q+\frac{8}{11}x+\frac{16}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{20}{13}+b)(\frac{14}{8}-q)& =(\color{red}{b}+\color{orange}{\frac{20}{13}}).(\color{green}{-q}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{20}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{20}{13})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{7}{4}b-\frac{20}{13}q+\frac{20}{13}.\frac{7}{4}& \text{Uitwerken } \\ & =-bq+\frac{7}{4}b-\frac{20}{13}q+\frac{140}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{7}{4}b-\frac{20}{13}q+\frac{35}{13} & \text{Vereenvoudig} \\\end{align}\)
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