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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{8}{15})(\frac{-15}{3}-a)& =(\color{red}{a}+\color{orange}{\frac{8}{15}}).(\color{green}{-a}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(-5)} + \color{orange}{(\frac{8}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -aa-5a-\frac{8}{15}a-\frac{8}{15}.5& \text{Uitwerken } \\ & =-a^2+((-5)+(\frac{-8}{15}))a-\frac{40}{15} & \text{Neem samen} \\ &=-a^2-\frac{83}{15}a-\frac{40}{15} & \text{Maak de som} \\ &=-a^2-\frac{83}{15}a-\frac{8}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-19}{7}-a)(x-\frac{7}{16})& =(\color{red}{-a}+\color{orange}{\frac{-19}{7}}).(\color{green}{x}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{16}a-\frac{19}{7}x+\frac{19}{7}.\frac{7}{16}& \text{Uitwerken } \\ & =-ax+\frac{7}{16}a-\frac{19}{7}x+\frac{133}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{7}{16}a-\frac{19}{7}x+\frac{19}{16} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{16}{19}-x)(p-\frac{-11}{18})& =(\color{red}{-x}+\color{orange}{\frac{16}{19}}).(\color{green}{p}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(\frac{16}{19})} . \color{green}{(p)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{11}{18}x+\frac{16}{19}p+\frac{16}{19}.\frac{11}{18}& \text{Uitwerken } \\ & =-px-\frac{11}{18}x+\frac{16}{19}p+\frac{176}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{11}{18}x+\frac{16}{19}p+\frac{88}{171} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{9}+b)(p-\frac{-5}{14})& =(\color{red}{b}+\color{orange}{\frac{11}{9}}).(\color{green}{p}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{11}{9})} . \color{green}{(p)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{14}b+\frac{11}{9}p+\frac{11}{9}.\frac{5}{14}& \text{Uitwerken } \\ & =bp+\frac{5}{14}b+\frac{11}{9}p+\frac{55}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-7}{2})(a+\frac{17}{8})& =(\color{red}{p}+\color{orange}{\frac{7}{2}}).(\color{green}{a}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{7}{2})} . \color{green}{(a)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{8}p+\frac{7}{2}a+\frac{7}{2}.\frac{17}{8}& \text{Uitwerken } \\ & =ap+\frac{17}{8}p+\frac{7}{2}a+\frac{119}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{5}{16}-a)(\frac{-19}{6}-b)& =(\color{red}{-a}+\color{orange}{\frac{5}{16}}).(\color{green}{-b}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{5}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{6}a-\frac{5}{16}b-\frac{5}{16}.\frac{19}{6}& \text{Uitwerken } \\ & =ab+\frac{19}{6}a-\frac{5}{16}b-\frac{95}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{14}{13})(q+\frac{19}{17})& =(\color{red}{x}+\color{orange}{\frac{-14}{13}}).(\color{green}{q}+\color{blue}{\frac{19}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{19}{17})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{19}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{17}x-\frac{14}{13}q-\frac{14}{13}.\frac{19}{17}& \text{Uitwerken } \\ & =qx+\frac{19}{17}x-\frac{14}{13}q-\frac{266}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-11}{5})(p+\frac{-14}{6})& =(\color{red}{b}+\color{orange}{\frac{-11}{5}}).(\color{green}{p}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{3}b-\frac{11}{5}p+\frac{11}{5}.\frac{7}{3}& \text{Uitwerken } \\ & =bp-\frac{7}{3}b-\frac{11}{5}p+\frac{77}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{19}{10}+a)(x+1)& =(\color{red}{a}+\color{orange}{\frac{19}{10}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{19}{10})} . \color{green}{(x)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1a+\frac{19}{10}x+\frac{19}{10}.1& \text{Uitwerken } \\ & =ax+1a+\frac{19}{10}x+\frac{19}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-2}{14}+p)(q-\frac{-8}{3})& =(\color{red}{p}+\color{orange}{\frac{-1}{7}}).(\color{green}{q}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{3}p-\frac{1}{7}q-\frac{1}{7}.\frac{8}{3}& \text{Uitwerken } \\ & =pq+\frac{8}{3}p-\frac{1}{7}q-\frac{8}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{13}{18}-b)(\frac{-15}{8}-x)& =(\color{red}{-b}+\color{orange}{\frac{13}{18}}).(\color{green}{-x}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{13}{18})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{8}b-\frac{13}{18}x-\frac{13}{18}.\frac{15}{8}& \text{Uitwerken } \\ & =bx+\frac{15}{8}b-\frac{13}{18}x-\frac{195}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{15}{8}b-\frac{13}{18}x-\frac{65}{48} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p-\frac{16}{10})(p+\frac{-1}{19})& =(\color{red}{p}+\color{orange}{\frac{-8}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{19}p-\frac{8}{5}p+\frac{8}{5}.\frac{1}{19}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{19})+(\frac{-8}{5}))p+\frac{8}{95} & \text{Neem samen} \\ &=p^2-\frac{157}{95}p+\frac{8}{95} & \text{Maak de som} \\\end{align}\)
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