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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{1}{17}+x)(\frac{14}{4}+q)& =(\color{red}{x}+\color{orange}{\frac{1}{17}}).(\color{green}{q}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{1}{17})} . \color{green}{(q)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{2}x+\frac{1}{17}q+\frac{1}{17}.\frac{7}{2}& \text{Uitwerken } \\ & =qx+\frac{7}{2}x+\frac{1}{17}q+\frac{7}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{16}{7}-p)(p-\frac{8}{12})& =(\color{red}{-p}+\color{orange}{\frac{16}{7}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{16}{7})} . \color{green}{(p)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{2}{3}p+\frac{16}{7}p-\frac{16}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{2}{3}+\frac{16}{7})p-\frac{32}{21} & \text{Neem samen} \\ &=-p^2+\frac{62}{21}p-\frac{32}{21} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-7}{12}-p)(\frac{-18}{9}+x)& =(\color{red}{-p}+\color{orange}{\frac{-7}{12}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{12})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -px+2p-\frac{7}{12}x+\frac{7}{12}.2& \text{Uitwerken } \\ & =-px+2p-\frac{7}{12}x+\frac{14}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+2p-\frac{7}{12}x+\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-12}{12})(a+\frac{-8}{14})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{4}{7}a+1a-1.\frac{4}{7}& \text{Uitwerken } \\ & =a^2+((\frac{-4}{7})+1)a-(\frac{-4}{7}) & \text{Neem samen} \\ &=a^2+\frac{3}{7}a-(\frac{-4}{7}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{20}-x)(\frac{19}{4}+b)& =(\color{red}{-x}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{19}{4}x+\frac{4}{5}b+\frac{4}{5}.\frac{19}{4}& \text{Uitwerken } \\ & =-bx-\frac{19}{4}x+\frac{4}{5}b+\frac{76}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{19}{4}x+\frac{4}{5}b+\frac{19}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+(-6))(q+\frac{19}{15})& =(\color{red}{x}+\color{orange}{(-6)}).(\color{green}{q}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(-6)} . \color{green}{(q)} + \color{orange}{(-6)} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{15}x-6q-6.\frac{19}{15}& \text{Uitwerken } \\ & =qx+\frac{19}{15}x-6q-\frac{114}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{19}{15}x-6q-\frac{38}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-18}{16})(\frac{-2}{6}-a)& =(\color{red}{b}+\color{orange}{\frac{-9}{8}}).(\color{green}{-a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{3}b+\frac{9}{8}a+\frac{9}{8}.\frac{1}{3}& \text{Uitwerken } \\ & =-ab-\frac{1}{3}b+\frac{9}{8}a+\frac{9}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{1}{3}b+\frac{9}{8}a+\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p-\frac{13}{16})(x+\frac{8}{10})& =(\color{red}{p}+\color{orange}{\frac{-13}{16}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{4}{5}p-\frac{13}{16}x-\frac{13}{16}.\frac{4}{5}& \text{Uitwerken } \\ & =px+\frac{4}{5}p-\frac{13}{16}x-\frac{52}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{4}{5}p-\frac{13}{16}x-\frac{13}{20} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{20}{8}-q)(a+\frac{-12}{12})& =(\color{red}{-q}+\color{orange}{\frac{5}{2}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq+1q+\frac{5}{2}a-\frac{5}{2}.1& \text{Uitwerken } \\ & =-aq+1q+\frac{5}{2}a-\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-16}{14})(\frac{6}{9}+x)& =(\color{red}{q}+\color{orange}{\frac{-8}{7}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{3}q-\frac{8}{7}x-\frac{8}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =qx+\frac{2}{3}q-\frac{8}{7}x-\frac{16}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}((-3)+b)(\frac{5}{4}+b)& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{4}b-3b-3.\frac{5}{4}& \text{Uitwerken } \\ & =b^2+(\frac{5}{4}+(-3))b-(\frac{-15}{4}) & \text{Neem samen} \\ &=b^2-\frac{7}{4}b-(\frac{-15}{4}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q-\frac{13}{7})(a-\frac{20}{16})& =(\color{red}{q}+\color{orange}{\frac{-13}{7}}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{4}q-\frac{13}{7}a+\frac{13}{7}.\frac{5}{4}& \text{Uitwerken } \\ & =aq-\frac{5}{4}q-\frac{13}{7}a+\frac{65}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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