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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{15}-q)(q+\frac{3}{13})& =(\color{red}{-q}+\color{orange}{\frac{4}{3}}).(\color{green}{q}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{3}{13}q+\frac{4}{3}q+\frac{4}{3}.\frac{3}{13}& \text{Uitwerken } \\ & =-q^2+((\frac{-3}{13})+\frac{4}{3})q+(\frac{-12}{39}) & \text{Neem samen} \\ &=-q^2+\frac{43}{39}q+(\frac{-12}{39}) & \text{Maak de som} \\ &=-q^2+\frac{43}{39}q+(\frac{-4}{13}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(x+\frac{16}{14})(\frac{13}{13}-x)& =(\color{red}{x}+\color{orange}{\frac{8}{7}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{8}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -xx+1x-\frac{8}{7}x+\frac{8}{7}.1& \text{Uitwerken } \\ & =-x^2+(1+(\frac{-8}{7}))x+(\frac{-8}{7}) & \text{Neem samen} \\ &=-x^2-\frac{1}{7}x+(\frac{-8}{7}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}((-13)-q)(\frac{18}{14}+p)& =(\color{red}{-q}+\color{orange}{(-13)}).(\color{green}{p}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(-13)} . \color{green}{(p)} + \color{orange}{(-13)} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{7}q-13p-13.\frac{9}{7}& \text{Uitwerken } \\ & =-pq-\frac{9}{7}q-13p-\frac{117}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{19}{11})(\frac{-16}{16}-b)& =(\color{red}{a}+\color{orange}{\frac{19}{11}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{19}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ab-1a-\frac{19}{11}b-\frac{19}{11}.1& \text{Uitwerken } \\ & =-ab-1a-\frac{19}{11}b-\frac{19}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{20}{16})(\frac{3}{9}-p)& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{-p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{3}a+\frac{5}{4}p-\frac{5}{4}.\frac{1}{3}& \text{Uitwerken } \\ & =-ap+\frac{1}{3}a+\frac{5}{4}p-\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-19}{20})(\frac{-10}{11}+b)& =(\color{red}{b}+\color{orange}{\frac{19}{20}}).(\color{green}{b}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{19}{20})} . \color{green}{(b)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{10}{11}b+\frac{19}{20}b-\frac{19}{20}.\frac{10}{11}& \text{Uitwerken } \\ & =b^2+((\frac{-10}{11})+\frac{19}{20})b-(\frac{-190}{220}) & \text{Neem samen} \\ &=b^2+\frac{9}{220}b-(\frac{-190}{220}) & \text{Maak de som} \\ &=b^2+\frac{9}{220}b+\frac{19}{22} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(x+\frac{3}{6})(b+\frac{2}{4})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}x+\frac{1}{2}b+\frac{1}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}x+\frac{1}{2}b+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{14}{20})(x-\frac{14}{8})& =(\color{red}{p}+\color{orange}{\frac{7}{10}}).(\color{green}{x}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{7}{10})} . \color{green}{(x)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{4}p+\frac{7}{10}x-\frac{7}{10}.\frac{7}{4}& \text{Uitwerken } \\ & =px-\frac{7}{4}p+\frac{7}{10}x-\frac{49}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-4}{3}-b)(q+\frac{4}{17})& =(\color{red}{-b}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{4}{17}b-\frac{4}{3}q-\frac{4}{3}.\frac{4}{17}& \text{Uitwerken } \\ & =-bq-\frac{4}{17}b-\frac{4}{3}q-\frac{16}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-20}{8}+p)(b+\frac{-16}{3})& =(\color{red}{p}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{16}{3}p-\frac{5}{2}b+\frac{5}{2}.\frac{16}{3}& \text{Uitwerken } \\ & =bp-\frac{16}{3}p-\frac{5}{2}b+\frac{80}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{16}{3}p-\frac{5}{2}b+\frac{40}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-2}{10}-p)(\frac{1}{8}+p)& =(\color{red}{-p}+\color{orange}{\frac{-1}{5}}).(\color{green}{p}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{8}p-\frac{1}{5}p-\frac{1}{5}.\frac{1}{8}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{8})+(\frac{-1}{5}))p-\frac{1}{40} & \text{Neem samen} \\ &=-p^2-\frac{13}{40}p-\frac{1}{40} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-19}{9})(q+\frac{-18}{6})& =(\color{red}{p}+\color{orange}{\frac{-19}{9}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{-19}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = pq-3p-\frac{19}{9}q+\frac{19}{9}.3& \text{Uitwerken } \\ & =pq-3p-\frac{19}{9}q+\frac{57}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-3p-\frac{19}{9}q+\frac{19}{3} & \text{Vereenvoudig} \\\end{align}\)
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