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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-14}{6})(\frac{-17}{13}-b)& =(\color{red}{a}+\color{orange}{\frac{-7}{3}}).(\color{green}{-b}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{17}{13}a+\frac{7}{3}b+\frac{7}{3}.\frac{17}{13}& \text{Uitwerken } \\ & =-ab-\frac{17}{13}a+\frac{7}{3}b+\frac{119}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{4}+q)(b-\frac{-17}{18})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{18}q-3b-3.\frac{17}{18}& \text{Uitwerken } \\ & =bq+\frac{17}{18}q-3b-\frac{51}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{17}{18}q-3b-\frac{17}{6} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{19}{15})(\frac{7}{8}-q)& =(\color{red}{q}+\color{orange}{\frac{19}{15}}).(\color{green}{-q}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{19}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{7}{8}q-\frac{19}{15}q+\frac{19}{15}.\frac{7}{8}& \text{Uitwerken } \\ & =-q^2+(\frac{7}{8}+(\frac{-19}{15}))q+(\frac{-133}{120}) & \text{Neem samen} \\ &=-q^2-\frac{47}{120}q+(\frac{-133}{120}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-5}{11}-b)(q-\frac{-6}{4})& =(\color{red}{-b}+\color{orange}{\frac{-5}{11}}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{2}b-\frac{5}{11}q-\frac{5}{11}.\frac{3}{2}& \text{Uitwerken } \\ & =-bq-\frac{3}{2}b-\frac{5}{11}q-\frac{15}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{17}-p)(b+\frac{-18}{17})& =(\color{red}{-p}+\color{orange}{\frac{5}{17}}).(\color{green}{b}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{5}{17})} . \color{green}{(b)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{18}{17}p+\frac{5}{17}b-\frac{5}{17}.\frac{18}{17}& \text{Uitwerken } \\ & =-bp+\frac{18}{17}p+\frac{5}{17}b-\frac{90}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-5}{16})(\frac{-16}{17}-x)& =(\color{red}{p}+\color{orange}{\frac{-5}{16}}).(\color{green}{-x}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{-5}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{16}{17}p+\frac{5}{16}x+\frac{5}{16}.\frac{16}{17}& \text{Uitwerken } \\ & =-px-\frac{16}{17}p+\frac{5}{16}x+\frac{80}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{16}{17}p+\frac{5}{16}x+\frac{5}{17} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-3}{18}+a)(\frac{-12}{3}-p)& =(\color{red}{a}+\color{orange}{\frac{-1}{6}}).(\color{green}{-p}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ap-4a+\frac{1}{6}p+\frac{1}{6}.4& \text{Uitwerken } \\ & =-ap-4a+\frac{1}{6}p+\frac{4}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-4a+\frac{1}{6}p+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p-\frac{13}{10})(p+\frac{-10}{10})& =(\color{red}{p}+\color{orange}{\frac{-13}{10}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-13}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pp-1p-\frac{13}{10}p+\frac{13}{10}.1& \text{Uitwerken } \\ & =p^2+((-1)+(\frac{-13}{10}))p+\frac{13}{10} & \text{Neem samen} \\ &=p^2-\frac{23}{10}p+\frac{13}{10} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{7}{14}+b)(q+\frac{-12}{11})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{12}{11}b+\frac{1}{2}q-\frac{1}{2}.\frac{12}{11}& \text{Uitwerken } \\ & =bq-\frac{12}{11}b+\frac{1}{2}q-\frac{12}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{12}{11}b+\frac{1}{2}q-\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{5}{12}+a)(q+\frac{-3}{15})& =(\color{red}{a}+\color{orange}{\frac{5}{12}}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{5}{12})} . \color{green}{(q)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{5}a+\frac{5}{12}q-\frac{5}{12}.\frac{1}{5}& \text{Uitwerken } \\ & =aq-\frac{1}{5}a+\frac{5}{12}q-\frac{5}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{5}a+\frac{5}{12}q-\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-5}{12})(x+\frac{12}{17})& =(\color{red}{x}+\color{orange}{\frac{-5}{12}}).(\color{green}{x}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{-5}{12})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{12})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{12}{17}x-\frac{5}{12}x-\frac{5}{12}.\frac{12}{17}& \text{Uitwerken } \\ & =x^2+(\frac{12}{17}+(\frac{-5}{12}))x-(\frac{-60}{204}) & \text{Neem samen} \\ &=x^2+\frac{59}{204}x-(\frac{-60}{204}) & \text{Maak de som} \\ &=x^2+\frac{59}{204}x+\frac{5}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(x+(-8))(\frac{-2}{8}-a)& =(\color{red}{x}+\color{orange}{(-8)}).(\color{green}{-a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(-8)} . \color{green}{(-a)} + \color{orange}{(-8)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{4}x+8a+8.\frac{1}{4}& \text{Uitwerken } \\ & =-ax-\frac{1}{4}x+8a+\frac{8}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{1}{4}x+8a+2 & \text{Vereenvoudig} \\\end{align}\)
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