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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-9}{17}-a)(q-\frac{-18}{5})& =(\color{red}{-a}+\color{orange}{\frac{-9}{17}}).(\color{green}{q}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{18}{5}a-\frac{9}{17}q-\frac{9}{17}.\frac{18}{5}& \text{Uitwerken } \\ & =-aq-\frac{18}{5}a-\frac{9}{17}q-\frac{162}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-20}{3}+b)(\frac{10}{18}-q)& =(\color{red}{b}+\color{orange}{\frac{-20}{3}}).(\color{green}{-q}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{9}b+\frac{20}{3}q-\frac{20}{3}.\frac{5}{9}& \text{Uitwerken } \\ & =-bq+\frac{5}{9}b+\frac{20}{3}q-\frac{100}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-4}{2})(\frac{5}{7}+q)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{7}a+2q+2.\frac{5}{7}& \text{Uitwerken } \\ & =aq+\frac{5}{7}a+2q+\frac{10}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-7}{9}-a)(\frac{-2}{12}+q)& =(\color{red}{-a}+\color{orange}{\frac{-7}{9}}).(\color{green}{q}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{6}a-\frac{7}{9}q+\frac{7}{9}.\frac{1}{6}& \text{Uitwerken } \\ & =-aq+\frac{1}{6}a-\frac{7}{9}q+\frac{7}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{13}{15})(\frac{-12}{6}-p)& =(\color{red}{x}+\color{orange}{\frac{-13}{15}}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-13}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -px-2x+\frac{13}{15}p+\frac{13}{15}.2& \text{Uitwerken } \\ & =-px-2x+\frac{13}{15}p+\frac{26}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-18}{7})(\frac{15}{2}+b)& =(\color{red}{a}+\color{orange}{\frac{-18}{7}}).(\color{green}{b}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{15}{2}a-\frac{18}{7}b-\frac{18}{7}.\frac{15}{2}& \text{Uitwerken } \\ & =ab+\frac{15}{2}a-\frac{18}{7}b-\frac{270}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{15}{2}a-\frac{18}{7}b-\frac{135}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a+\frac{5}{16})(\frac{-3}{14}-a)& =(\color{red}{a}+\color{orange}{\frac{5}{16}}).(\color{green}{-a}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{5}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{3}{14}a-\frac{5}{16}a-\frac{5}{16}.\frac{3}{14}& \text{Uitwerken } \\ & =-a^2+((\frac{-3}{14})+(\frac{-5}{16}))a-\frac{15}{224} & \text{Neem samen} \\ &=-a^2-\frac{59}{112}a-\frac{15}{224} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{17}{9}+p)(\frac{7}{5}+p)& =(\color{red}{p}+\color{orange}{\frac{17}{9}}).(\color{green}{p}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{17}{9})} . \color{green}{(p)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{7}{5}p+\frac{17}{9}p+\frac{17}{9}.\frac{7}{5}& \text{Uitwerken } \\ & =p^2+(\frac{7}{5}+\frac{17}{9})p+\frac{119}{45} & \text{Neem samen} \\ &=p^2+\frac{148}{45}p+\frac{119}{45} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-2}{14})(\frac{2}{4}-x)& =(\color{red}{a}+\color{orange}{\frac{-1}{7}}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{2}a+\frac{1}{7}x-\frac{1}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =-ax+\frac{1}{2}a+\frac{1}{7}x-\frac{1}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{13}{13})(p-\frac{-1}{17})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{17}b-1p-1.\frac{1}{17}& \text{Uitwerken } \\ & =bp+\frac{1}{17}b-1p-\frac{1}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{5}{19}+p)(\frac{-14}{12}-b)& =(\color{red}{p}+\color{orange}{\frac{5}{19}}).(\color{green}{-b}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{5}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{6}p-\frac{5}{19}b-\frac{5}{19}.\frac{7}{6}& \text{Uitwerken } \\ & =-bp-\frac{7}{6}p-\frac{5}{19}b-\frac{35}{114} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-14}{4}+p)(q-\frac{16}{11})& =(\color{red}{p}+\color{orange}{\frac{-7}{2}}).(\color{green}{q}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{16}{11}p-\frac{7}{2}q+\frac{7}{2}.\frac{16}{11}& \text{Uitwerken } \\ & =pq-\frac{16}{11}p-\frac{7}{2}q+\frac{112}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{16}{11}p-\frac{7}{2}q+\frac{56}{11} & \text{Vereenvoudig} \\\end{align}\)
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