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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{5}{16})(a+\frac{3}{11})& =(\color{red}{x}+\color{orange}{\frac{5}{16}}).(\color{green}{a}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{11})} + \color{orange}{(\frac{5}{16})} . \color{green}{(a)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{11}x+\frac{5}{16}a+\frac{5}{16}.\frac{3}{11}& \text{Uitwerken } \\ & =ax+\frac{3}{11}x+\frac{5}{16}a+\frac{15}{176} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-10}{19}-b)(p+\frac{20}{5})& =(\color{red}{-b}+\color{orange}{\frac{-10}{19}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(4)} + \color{orange}{(\frac{-10}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -bp-4b-\frac{10}{19}p-\frac{10}{19}.4& \text{Uitwerken } \\ & =-bp-4b-\frac{10}{19}p-\frac{40}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-7}{17}-x)(p+\frac{1}{15})& =(\color{red}{-x}+\color{orange}{\frac{-7}{17}}).(\color{green}{p}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{15}x-\frac{7}{17}p-\frac{7}{17}.\frac{1}{15}& \text{Uitwerken } \\ & =-px-\frac{1}{15}x-\frac{7}{17}p-\frac{7}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(10-q)(p-\frac{-16}{20})& =(\color{red}{-q}+\color{orange}{10}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(10)} . \color{green}{(p)} + \color{orange}{(10)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{4}{5}q+10p+10.\frac{4}{5}& \text{Uitwerken } \\ & =-pq-\frac{4}{5}q+10p+\frac{40}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{4}{5}q+10p+8 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-7}{13})(p+\frac{16}{17})& =(\color{red}{q}+\color{orange}{\frac{7}{13}}).(\color{green}{p}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{7}{13})} . \color{green}{(p)} + \color{orange}{(\frac{7}{13})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{16}{17}q+\frac{7}{13}p+\frac{7}{13}.\frac{16}{17}& \text{Uitwerken } \\ & =pq+\frac{16}{17}q+\frac{7}{13}p+\frac{112}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{9}{6})(\frac{6}{6}-p)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1b+\frac{3}{2}p-\frac{3}{2}.1& \text{Uitwerken } \\ & =-bp+1b+\frac{3}{2}p-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-17}{5}-p)(p-\frac{19}{4})& =(\color{red}{-p}+\color{orange}{\frac{-17}{5}}).(\color{green}{p}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{19}{4}p-\frac{17}{5}p+\frac{17}{5}.\frac{19}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{19}{4}+(\frac{-17}{5}))p+(\frac{-323}{20}) & \text{Neem samen} \\ &=-p^2+\frac{27}{20}p+(\frac{-323}{20}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-11}{20})(x-\frac{-17}{13})& =(\color{red}{p}+\color{orange}{\frac{11}{20}}).(\color{green}{x}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{11}{20})} . \color{green}{(x)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{13}p+\frac{11}{20}x+\frac{11}{20}.\frac{17}{13}& \text{Uitwerken } \\ & =px+\frac{17}{13}p+\frac{11}{20}x+\frac{187}{260} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{13}{2}-q)(\frac{-17}{19}+b)& =(\color{red}{-q}+\color{orange}{\frac{13}{2}}).(\color{green}{b}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(\frac{13}{2})} . \color{green}{(b)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{17}{19}q+\frac{13}{2}b-\frac{13}{2}.\frac{17}{19}& \text{Uitwerken } \\ & =-bq+\frac{17}{19}q+\frac{13}{2}b-\frac{221}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-18}{11}+a)(p-\frac{19}{9})& =(\color{red}{a}+\color{orange}{\frac{-18}{11}}).(\color{green}{p}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-18}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{11})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{9}a-\frac{18}{11}p+\frac{18}{11}.\frac{19}{9}& \text{Uitwerken } \\ & =ap-\frac{19}{9}a-\frac{18}{11}p+\frac{342}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{19}{9}a-\frac{18}{11}p+\frac{38}{11} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{18}{8})(\frac{-9}{10}+p)& =(\color{red}{x}+\color{orange}{\frac{-9}{4}}).(\color{green}{p}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{10}x-\frac{9}{4}p+\frac{9}{4}.\frac{9}{10}& \text{Uitwerken } \\ & =px-\frac{9}{10}x-\frac{9}{4}p+\frac{81}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{19}{15})(\frac{11}{20}-a)& =(\color{red}{a}+\color{orange}{\frac{19}{15}}).(\color{green}{-a}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{19}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{11}{20}a-\frac{19}{15}a+\frac{19}{15}.\frac{11}{20}& \text{Uitwerken } \\ & =-a^2+(\frac{11}{20}+(\frac{-19}{15}))a+(\frac{-209}{300}) & \text{Neem samen} \\ &=-a^2-\frac{43}{60}a+(\frac{-209}{300}) & \text{Maak de som} \\\end{align}\)
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