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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-2}{20}+b)(\frac{-3}{16}+p)& =(\color{red}{b}+\color{orange}{\frac{-1}{10}}).(\color{green}{p}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{16}b-\frac{1}{10}p+\frac{1}{10}.\frac{3}{16}& \text{Uitwerken } \\ & =bp-\frac{3}{16}b-\frac{1}{10}p+\frac{3}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-8}{17}+q)(x-\frac{-17}{8})& =(\color{red}{q}+\color{orange}{\frac{-8}{17}}).(\color{green}{x}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{8}q-\frac{8}{17}x-\frac{8}{17}.\frac{17}{8}& \text{Uitwerken } \\ & =qx+\frac{17}{8}q-\frac{8}{17}x-\frac{136}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{17}{8}q-\frac{8}{17}x-1 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+\frac{8}{5})(\frac{19}{19}-q)& =(\color{red}{b}+\color{orange}{\frac{8}{5}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{8}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bq+1b-\frac{8}{5}q+\frac{8}{5}.1& \text{Uitwerken } \\ & =-bq+1b-\frac{8}{5}q+\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-13}{11})(\frac{16}{10}-a)& =(\color{red}{q}+\color{orange}{\frac{13}{11}}).(\color{green}{-a}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{13}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{8}{5}q-\frac{13}{11}a+\frac{13}{11}.\frac{8}{5}& \text{Uitwerken } \\ & =-aq+\frac{8}{5}q-\frac{13}{11}a+\frac{104}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-19}{19})(p+\frac{-10}{5})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = px-2x-1p+1.2& \text{Uitwerken } \\ & =px-2x-1p+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-3}{10})(a+\frac{-6}{10})& =(\color{red}{q}+\color{orange}{\frac{3}{10}}).(\color{green}{a}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{5}q+\frac{3}{10}a-\frac{3}{10}.\frac{3}{5}& \text{Uitwerken } \\ & =aq-\frac{3}{5}q+\frac{3}{10}a-\frac{9}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-15}{20})(\frac{-18}{2}-p)& =(\color{red}{b}+\color{orange}{\frac{-3}{4}}).(\color{green}{-p}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-9)} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -bp-9b+\frac{3}{4}p+\frac{3}{4}.9& \text{Uitwerken } \\ & =-bp-9b+\frac{3}{4}p+\frac{27}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-11}{9})(\frac{5}{5}-a)& =(\color{red}{b}+\color{orange}{\frac{-11}{9}}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-11}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ab+1b+\frac{11}{9}a-\frac{11}{9}.1& \text{Uitwerken } \\ & =-ab+1b+\frac{11}{9}a-\frac{11}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+\frac{7}{5})(q-\frac{-18}{3})& =(\color{red}{p}+\color{orange}{\frac{7}{5}}).(\color{green}{q}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(6)} + \color{orange}{(\frac{7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = pq+6p+\frac{7}{5}q+\frac{7}{5}.6& \text{Uitwerken } \\ & =pq+6p+\frac{7}{5}q+\frac{42}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-9}{6}-b)(p-\frac{18}{17})& =(\color{red}{-b}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{18}{17}b-\frac{3}{2}p+\frac{3}{2}.\frac{18}{17}& \text{Uitwerken } \\ & =-bp+\frac{18}{17}b-\frac{3}{2}p+\frac{54}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{18}{17}b-\frac{3}{2}p+\frac{27}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-10}{17})(q+\frac{-19}{15})& =(\color{red}{p}+\color{orange}{\frac{10}{17}}).(\color{green}{q}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{10}{17})} . \color{green}{(q)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{15}p+\frac{10}{17}q-\frac{10}{17}.\frac{19}{15}& \text{Uitwerken } \\ & =pq-\frac{19}{15}p+\frac{10}{17}q-\frac{190}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{19}{15}p+\frac{10}{17}q-\frac{38}{51} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{12}-a)(\frac{-6}{12}+a)& =(\color{red}{-a}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{2}a-\frac{3}{2}a+\frac{3}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{2}+(\frac{-3}{2}))a+(\frac{-3}{4}) & \text{Neem samen} \\ &=-a^2-\frac{2}{2}a+(\frac{-3}{4}) & \text{Maak de som} \\ &=-a^2-1a+(\frac{-3}{4}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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