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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{9}-p)(\frac{15}{15}-b)& =(\color{red}{-p}+\color{orange}{\frac{-19}{9}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp-1p+\frac{19}{9}b-\frac{19}{9}.1& \text{Uitwerken } \\ & =bp-1p+\frac{19}{9}b-\frac{19}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{11}-q)(\frac{11}{20}+a)& =(\color{red}{-q}+\color{orange}{\frac{20}{11}}).(\color{green}{a}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{20}{11})} . \color{green}{(a)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{11}{20}q+\frac{20}{11}a+\frac{20}{11}.\frac{11}{20}& \text{Uitwerken } \\ & =-aq-\frac{11}{20}q+\frac{20}{11}a+\frac{220}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{11}{20}q+\frac{20}{11}a+1 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-17}{3})(\frac{8}{18}-x)& =(\color{red}{x}+\color{orange}{\frac{17}{3}}).(\color{green}{-x}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{17}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{3})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{4}{9}x-\frac{17}{3}x+\frac{17}{3}.\frac{4}{9}& \text{Uitwerken } \\ & =-x^2+(\frac{4}{9}+(\frac{-17}{3}))x+(\frac{-68}{27}) & \text{Neem samen} \\ &=-x^2-\frac{47}{9}x+(\frac{-68}{27}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{8}{17}+p)(x-\frac{-2}{7})& =(\color{red}{p}+\color{orange}{\frac{8}{17}}).(\color{green}{x}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{8}{17})} . \color{green}{(x)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{2}{7}p+\frac{8}{17}x+\frac{8}{17}.\frac{2}{7}& \text{Uitwerken } \\ & =px+\frac{2}{7}p+\frac{8}{17}x+\frac{16}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{11}{18}+a)(p-\frac{-19}{9})& =(\color{red}{a}+\color{orange}{\frac{11}{18}}).(\color{green}{p}+\color{blue}{\frac{19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{19}{9})} + \color{orange}{(\frac{11}{18})} . \color{green}{(p)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{19}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{9}a+\frac{11}{18}p+\frac{11}{18}.\frac{19}{9}& \text{Uitwerken } \\ & =ap+\frac{19}{9}a+\frac{11}{18}p+\frac{209}{162} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-8}{9}+q)(b-\frac{-5}{5})& =(\color{red}{q}+\color{orange}{\frac{-8}{9}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{-8}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1q-\frac{8}{9}b-\frac{8}{9}.1& \text{Uitwerken } \\ & =bq+1q-\frac{8}{9}b-\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{14}{3}+x)(p-\frac{-17}{16})& =(\color{red}{x}+\color{orange}{\frac{14}{3}}).(\color{green}{p}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{14}{3})} . \color{green}{(p)} + \color{orange}{(\frac{14}{3})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{16}x+\frac{14}{3}p+\frac{14}{3}.\frac{17}{16}& \text{Uitwerken } \\ & =px+\frac{17}{16}x+\frac{14}{3}p+\frac{238}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{17}{16}x+\frac{14}{3}p+\frac{119}{24} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{4}{8})(\frac{-18}{5}+p)& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{18}{5}x-\frac{1}{2}p+\frac{1}{2}.\frac{18}{5}& \text{Uitwerken } \\ & =px-\frac{18}{5}x-\frac{1}{2}p+\frac{18}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{18}{5}x-\frac{1}{2}p+\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{5}{14})(q+\frac{-8}{3})& =(\color{red}{b}+\color{orange}{\frac{-5}{14}}).(\color{green}{q}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{3}b-\frac{5}{14}q+\frac{5}{14}.\frac{8}{3}& \text{Uitwerken } \\ & =bq-\frac{8}{3}b-\frac{5}{14}q+\frac{40}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{8}{3}b-\frac{5}{14}q+\frac{20}{21} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-3}{2})(x-\frac{-17}{4})& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{4}q+\frac{3}{2}x+\frac{3}{2}.\frac{17}{4}& \text{Uitwerken } \\ & =qx+\frac{17}{4}q+\frac{3}{2}x+\frac{51}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-8}{7}+q)(q+\frac{1}{18})& =(\color{red}{q}+\color{orange}{\frac{-8}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{18}q-\frac{8}{7}q-\frac{8}{7}.\frac{1}{18}& \text{Uitwerken } \\ & =q^2+(\frac{1}{18}+(\frac{-8}{7}))q-(\frac{-8}{126}) & \text{Neem samen} \\ &=q^2-\frac{137}{126}q-(\frac{-8}{126}) & \text{Maak de som} \\ &=q^2-\frac{137}{126}q+\frac{4}{63} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{16}-a)(q-\frac{10}{4})& =(\color{red}{-a}+\color{orange}{\frac{-1}{8}}).(\color{green}{q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{2}a-\frac{1}{8}q+\frac{1}{8}.\frac{5}{2}& \text{Uitwerken } \\ & =-aq+\frac{5}{2}a-\frac{1}{8}q+\frac{5}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-11-23 08:56:37