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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{-17}{15})(p+\frac{-16}{3})& =(\color{red}{b}+\color{orange}{\frac{17}{15}}).(\color{green}{p}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{17}{15})} . \color{green}{(p)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{16}{3}b+\frac{17}{15}p-\frac{17}{15}.\frac{16}{3}& \text{Uitwerken } \\ & =bp-\frac{16}{3}b+\frac{17}{15}p-\frac{272}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-12}{10})(\frac{5}{6}-a)& =(\color{red}{a}+\color{orange}{\frac{-6}{5}}).(\color{green}{-a}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{5}{6}a+\frac{6}{5}a-\frac{6}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =-a^2+(\frac{5}{6}+\frac{6}{5})a-\frac{30}{30} & \text{Neem samen} \\ &=-a^2+\frac{61}{30}a-\frac{30}{30} & \text{Maak de som} \\ &=-a^2+\frac{61}{30}a-1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(b+(-5))(\frac{2}{19}-a)& =(\color{red}{b}+\color{orange}{(-5)}).(\color{green}{-a}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(-5)} . \color{green}{(-a)} + \color{orange}{(-5)} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{2}{19}b+5a-5.\frac{2}{19}& \text{Uitwerken } \\ & =-ab+\frac{2}{19}b+5a-\frac{10}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-11}{13}-p)(p-\frac{3}{5})& =(\color{red}{-p}+\color{orange}{\frac{-11}{13}}).(\color{green}{p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{3}{5}p-\frac{11}{13}p+\frac{11}{13}.\frac{3}{5}& \text{Uitwerken } \\ & =-p^2+(\frac{3}{5}+(\frac{-11}{13}))p+(\frac{-33}{65}) & \text{Neem samen} \\ &=-p^2-\frac{16}{65}p+(\frac{-33}{65}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a+\frac{4}{12})(b+\frac{-16}{4})& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ab-4a+\frac{1}{3}b-\frac{1}{3}.4& \text{Uitwerken } \\ & =ab-4a+\frac{1}{3}b-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-20}{6})(b+\frac{-5}{12})& =(\color{red}{a}+\color{orange}{\frac{-10}{3}}).(\color{green}{b}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{12}a-\frac{10}{3}b+\frac{10}{3}.\frac{5}{12}& \text{Uitwerken } \\ & =ab-\frac{5}{12}a-\frac{10}{3}b+\frac{50}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{12}a-\frac{10}{3}b+\frac{25}{18} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a-\frac{20}{2})(a-\frac{19}{11})& =(\color{red}{a}+\color{orange}{(-10)}).(\color{green}{a}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(-10)} . \color{green}{(a)} + \color{orange}{(-10)} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{19}{11}a-10a+10.\frac{19}{11}& \text{Uitwerken } \\ & =a^2+((\frac{-19}{11})+(-10))a+\frac{190}{11} & \text{Neem samen} \\ &=a^2-\frac{129}{11}a+\frac{190}{11} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{18}+x)(\frac{7}{15}+a)& =(\color{red}{x}+\color{orange}{\frac{2}{9}}).(\color{green}{a}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{2}{9})} . \color{green}{(a)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{15}x+\frac{2}{9}a+\frac{2}{9}.\frac{7}{15}& \text{Uitwerken } \\ & =ax+\frac{7}{15}x+\frac{2}{9}a+\frac{14}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-3}{17})(p-\frac{16}{6})& =(\color{red}{x}+\color{orange}{\frac{-3}{17}}).(\color{green}{p}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-3}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{8}{3}x-\frac{3}{17}p+\frac{3}{17}.\frac{8}{3}& \text{Uitwerken } \\ & =px-\frac{8}{3}x-\frac{3}{17}p+\frac{24}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{8}{3}x-\frac{3}{17}p+\frac{8}{17} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-16}{16}-p)(\frac{19}{17}+x)& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{19}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{17})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{19}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{17}p-1x-1.\frac{19}{17}& \text{Uitwerken } \\ & =-px-\frac{19}{17}p-1x-\frac{19}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-12}{14})(\frac{-8}{18}-q)& =(\color{red}{x}+\color{orange}{\frac{6}{7}}).(\color{green}{-q}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{6}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{4}{9}x-\frac{6}{7}q-\frac{6}{7}.\frac{4}{9}& \text{Uitwerken } \\ & =-qx-\frac{4}{9}x-\frac{6}{7}q-\frac{24}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{4}{9}x-\frac{6}{7}q-\frac{8}{21} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-5}{17}-a)(x-\frac{17}{10})& =(\color{red}{-a}+\color{orange}{\frac{-5}{17}}).(\color{green}{x}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{17}{10}a-\frac{5}{17}x+\frac{5}{17}.\frac{17}{10}& \text{Uitwerken } \\ & =-ax+\frac{17}{10}a-\frac{5}{17}x+\frac{85}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{17}{10}a-\frac{5}{17}x+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
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