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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-17}{11}+a)(b+\frac{-13}{17})& =(\color{red}{a}+\color{orange}{\frac{-17}{11}}).(\color{green}{b}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{-17}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{17}a-\frac{17}{11}b+\frac{17}{11}.\frac{13}{17}& \text{Uitwerken } \\ & =ab-\frac{13}{17}a-\frac{17}{11}b+\frac{221}{187} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{13}{17}a-\frac{17}{11}b+\frac{13}{11} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-19}{12}+x)(b-\frac{-19}{2})& =(\color{red}{x}+\color{orange}{\frac{-19}{12}}).(\color{green}{b}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{2}x-\frac{19}{12}b-\frac{19}{12}.\frac{19}{2}& \text{Uitwerken } \\ & =bx+\frac{19}{2}x-\frac{19}{12}b-\frac{361}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-10}{11})(q-\frac{8}{4})& =(\color{red}{b}+\color{orange}{\frac{-10}{11}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-10}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bq-2b-\frac{10}{11}q+\frac{10}{11}.2& \text{Uitwerken } \\ & =bq-2b-\frac{10}{11}q+\frac{20}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{19}{13})(\frac{4}{20}+b)& =(\color{red}{p}+\color{orange}{\frac{19}{13}}).(\color{green}{b}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{19}{13})} . \color{green}{(b)} + \color{orange}{(\frac{19}{13})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{5}p+\frac{19}{13}b+\frac{19}{13}.\frac{1}{5}& \text{Uitwerken } \\ & =bp+\frac{1}{5}p+\frac{19}{13}b+\frac{19}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-20)(x+\frac{-18}{20})& =(\color{red}{q}+\color{orange}{(-20)}).(\color{green}{x}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(-20)} . \color{green}{(x)} + \color{orange}{(-20)} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{10}q-20x+20.\frac{9}{10}& \text{Uitwerken } \\ & =qx-\frac{9}{10}q-20x+\frac{180}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{9}{10}q-20x+18 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-7}{16})(\frac{7}{18}+p)& =(\color{red}{b}+\color{orange}{\frac{7}{16}}).(\color{green}{p}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{7}{16})} . \color{green}{(p)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{18}b+\frac{7}{16}p+\frac{7}{16}.\frac{7}{18}& \text{Uitwerken } \\ & =bp+\frac{7}{18}b+\frac{7}{16}p+\frac{49}{288} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-13}{10})(\frac{-18}{9}-q)& =(\color{red}{b}+\color{orange}{\frac{13}{10}}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{13}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bq-2b-\frac{13}{10}q-\frac{13}{10}.2& \text{Uitwerken } \\ & =-bq-2b-\frac{13}{10}q-\frac{26}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-2b-\frac{13}{10}q-\frac{13}{5} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(7-p)(\frac{5}{3}+p)& =(\color{red}{-p}+\color{orange}{7}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(7)} . \color{green}{(p)} + \color{orange}{(7)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{5}{3}p+7p+7.\frac{5}{3}& \text{Uitwerken } \\ & =-p^2+((\frac{-5}{3})+7)p+(\frac{-35}{3}) & \text{Neem samen} \\ &=-p^2+\frac{16}{3}p+(\frac{-35}{3}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-8}{4}+q)(b+\frac{18}{15})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{6}{5}q-2b-2.\frac{6}{5}& \text{Uitwerken } \\ & =bq+\frac{6}{5}q-2b-\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{11}{12}-p)(p-\frac{13}{12})& =(\color{red}{-p}+\color{orange}{\frac{11}{12}}).(\color{green}{p}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{11}{12})} . \color{green}{(p)} + \color{orange}{(\frac{11}{12})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{13}{12}p+\frac{11}{12}p-\frac{11}{12}.\frac{13}{12}& \text{Uitwerken } \\ & =-p^2+(\frac{13}{12}+\frac{11}{12})p-\frac{143}{144} & \text{Neem samen} \\ &=-p^2+\frac{24}{12}p-\frac{143}{144} & \text{Maak de som} \\ &=-p^2+2p-\frac{143}{144} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(10-q)(\frac{-16}{19}+a)& =(\color{red}{-q}+\color{orange}{10}).(\color{green}{a}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(10)} . \color{green}{(a)} + \color{orange}{(10)} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{16}{19}q+10a-10.\frac{16}{19}& \text{Uitwerken } \\ & =-aq+\frac{16}{19}q+10a-\frac{160}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-5}{19})(\frac{18}{6}+q)& =(\color{red}{x}+\color{orange}{\frac{-5}{19}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{-5}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = qx+3x-\frac{5}{19}q-\frac{5}{19}.3& \text{Uitwerken } \\ & =qx+3x-\frac{5}{19}q-\frac{15}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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