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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{20}+b)(x-\frac{6}{18})& =(\color{red}{b}+\color{orange}{\frac{-13}{20}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{3}b-\frac{13}{20}x+\frac{13}{20}.\frac{1}{3}& \text{Uitwerken } \\ & =bx-\frac{1}{3}b-\frac{13}{20}x+\frac{13}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{6}{18}-x)(\frac{4}{2}+q)& =(\color{red}{-x}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(2)} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qx-2x+\frac{1}{3}q+\frac{1}{3}.2& \text{Uitwerken } \\ & =-qx-2x+\frac{1}{3}q+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{14}{14})(\frac{-2}{17}+q)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{17}x-1q+1.\frac{2}{17}& \text{Uitwerken } \\ & =qx-\frac{2}{17}x-1q+\frac{2}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-14}{7}-b)(\frac{20}{6}+b)& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{10}{3}b-2b-2.\frac{10}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-10}{3})+(-2))b-\frac{20}{3} & \text{Neem samen} \\ &=-b^2-\frac{16}{3}b-\frac{20}{3} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(q+\frac{8}{13})(p+\frac{11}{18})& =(\color{red}{q}+\color{orange}{\frac{8}{13}}).(\color{green}{p}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(\frac{8}{13})} . \color{green}{(p)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{18}q+\frac{8}{13}p+\frac{8}{13}.\frac{11}{18}& \text{Uitwerken } \\ & =pq+\frac{11}{18}q+\frac{8}{13}p+\frac{88}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{11}{18}q+\frac{8}{13}p+\frac{44}{117} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-11}{10}+p)(\frac{-1}{17}-b)& =(\color{red}{p}+\color{orange}{\frac{-11}{10}}).(\color{green}{-b}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{-11}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{17}p+\frac{11}{10}b+\frac{11}{10}.\frac{1}{17}& \text{Uitwerken } \\ & =-bp-\frac{1}{17}p+\frac{11}{10}b+\frac{11}{170} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{4}-q)(q+\frac{-1}{15})& =(\color{red}{-q}+\color{orange}{\frac{-9}{4}}).(\color{green}{q}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{1}{15}q-\frac{9}{4}q+\frac{9}{4}.\frac{1}{15}& \text{Uitwerken } \\ & =-q^2+(\frac{1}{15}+(\frac{-9}{4}))q+(\frac{-9}{60}) & \text{Neem samen} \\ &=-q^2-\frac{131}{60}q+(\frac{-9}{60}) & \text{Maak de som} \\ &=-q^2-\frac{131}{60}q+(\frac{-3}{20}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-13}{18}+b)(\frac{6}{6}-q)& =(\color{red}{b}+\color{orange}{\frac{-13}{18}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-13}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bq+1b+\frac{13}{18}q-\frac{13}{18}.1& \text{Uitwerken } \\ & =-bq+1b+\frac{13}{18}q-\frac{13}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{19}{9})(\frac{-20}{13}+p)& =(\color{red}{b}+\color{orange}{\frac{19}{9}}).(\color{green}{p}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{19}{9})} . \color{green}{(p)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{20}{13}b+\frac{19}{9}p-\frac{19}{9}.\frac{20}{13}& \text{Uitwerken } \\ & =bp-\frac{20}{13}b+\frac{19}{9}p-\frac{380}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{12}{12})(a-\frac{7}{16})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{16}b+1a-1.\frac{7}{16}& \text{Uitwerken } \\ & =ab-\frac{7}{16}b+1a-\frac{7}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{7}{4}-p)(\frac{-15}{16}+p)& =(\color{red}{-p}+\color{orange}{\frac{7}{4}}).(\color{green}{p}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{7}{4})} . \color{green}{(p)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{15}{16}p+\frac{7}{4}p-\frac{7}{4}.\frac{15}{16}& \text{Uitwerken } \\ & =-p^2+(\frac{15}{16}+\frac{7}{4})p-\frac{105}{64} & \text{Neem samen} \\ &=-p^2+\frac{43}{16}p-\frac{105}{64} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-16}{13}+x)(\frac{-2}{12}+q)& =(\color{red}{x}+\color{orange}{\frac{-16}{13}}).(\color{green}{q}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{6}x-\frac{16}{13}q+\frac{16}{13}.\frac{1}{6}& \text{Uitwerken } \\ & =qx-\frac{1}{6}x-\frac{16}{13}q+\frac{16}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{6}x-\frac{16}{13}q+\frac{8}{39} & \text{Vereenvoudig} \\\end{align}\)
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