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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{13}{4})(p+\frac{-12}{19})& =(\color{red}{b}+\color{orange}{\frac{-13}{4}}).(\color{green}{p}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{12}{19}b-\frac{13}{4}p+\frac{13}{4}.\frac{12}{19}& \text{Uitwerken } \\ & =bp-\frac{12}{19}b-\frac{13}{4}p+\frac{156}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{12}{19}b-\frac{13}{4}p+\frac{39}{19} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{9}{2}+q)(q-\frac{-2}{11})& =(\color{red}{q}+\color{orange}{\frac{9}{2}}).(\color{green}{q}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{9}{2})} . \color{green}{(q)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{2}{11}q+\frac{9}{2}q+\frac{9}{2}.\frac{2}{11}& \text{Uitwerken } \\ & =q^2+(\frac{2}{11}+\frac{9}{2})q+\frac{18}{22} & \text{Neem samen} \\ &=q^2+\frac{103}{22}q+\frac{18}{22} & \text{Maak de som} \\ &=q^2+\frac{103}{22}q+\frac{9}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{11}+p)(b+\frac{-16}{20})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{5}p-1b+1.\frac{4}{5}& \text{Uitwerken } \\ & =bp-\frac{4}{5}p-1b+\frac{4}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{8}{5})(\frac{7}{10}-p)& =(\color{red}{a}+\color{orange}{\frac{-8}{5}}).(\color{green}{-p}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{7}{10}a+\frac{8}{5}p-\frac{8}{5}.\frac{7}{10}& \text{Uitwerken } \\ & =-ap+\frac{7}{10}a+\frac{8}{5}p-\frac{56}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{7}{10}a+\frac{8}{5}p-\frac{28}{25} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-7}{4})(\frac{11}{15}+p)& =(\color{red}{a}+\color{orange}{\frac{-7}{4}}).(\color{green}{p}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{11}{15}a-\frac{7}{4}p-\frac{7}{4}.\frac{11}{15}& \text{Uitwerken } \\ & =ap+\frac{11}{15}a-\frac{7}{4}p-\frac{77}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-1}{5}-q)(x-\frac{16}{6})& =(\color{red}{-q}+\color{orange}{\frac{-1}{5}}).(\color{green}{x}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{8}{3}q-\frac{1}{5}x+\frac{1}{5}.\frac{8}{3}& \text{Uitwerken } \\ & =-qx+\frac{8}{3}q-\frac{1}{5}x+\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-19}{14})(b+\frac{-20}{10})& =(\color{red}{a}+\color{orange}{\frac{19}{14}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{19}{14})} . \color{green}{(b)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ab-2a+\frac{19}{14}b-\frac{19}{14}.2& \text{Uitwerken } \\ & =ab-2a+\frac{19}{14}b-\frac{38}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-2a+\frac{19}{14}b-\frac{19}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b-\frac{5}{2})(x+(-2))& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bx-2b-\frac{5}{2}x+\frac{5}{2}.2& \text{Uitwerken } \\ & =bx-2b-\frac{5}{2}x+\frac{10}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-2b-\frac{5}{2}x+5 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q-\frac{11}{7})(q+\frac{7}{16})& =(\color{red}{q}+\color{orange}{\frac{-11}{7}}).(\color{green}{q}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(\frac{-11}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{16}q-\frac{11}{7}q-\frac{11}{7}.\frac{7}{16}& \text{Uitwerken } \\ & =q^2+(\frac{7}{16}+(\frac{-11}{7}))q-(\frac{-77}{112}) & \text{Neem samen} \\ &=q^2-\frac{127}{112}q-(\frac{-77}{112}) & \text{Maak de som} \\ &=q^2-\frac{127}{112}q+\frac{11}{16} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(\frac{-1}{14}+x)(\frac{17}{7}+a)& =(\color{red}{x}+\color{orange}{\frac{-1}{14}}).(\color{green}{a}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{7}x-\frac{1}{14}a-\frac{1}{14}.\frac{17}{7}& \text{Uitwerken } \\ & =ax+\frac{17}{7}x-\frac{1}{14}a-\frac{17}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-2)(\frac{13}{7}-q)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{-q}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(-2)} . \color{green}{(-q)} + \color{orange}{(-2)} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{7}x+2q-2.\frac{13}{7}& \text{Uitwerken } \\ & =-qx+\frac{13}{7}x+2q-\frac{26}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{15}{16})(p-\frac{13}{18})& =(\color{red}{p}+\color{orange}{\frac{-15}{16}}).(\color{green}{p}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{13}{18}p-\frac{15}{16}p+\frac{15}{16}.\frac{13}{18}& \text{Uitwerken } \\ & =p^2+((\frac{-13}{18})+(\frac{-15}{16}))p+\frac{195}{288} & \text{Neem samen} \\ &=p^2-\frac{239}{144}p+\frac{195}{288} & \text{Maak de som} \\ &=p^2-\frac{239}{144}p+\frac{65}{96} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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