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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-14}{14}-q)(\frac{8}{6}+x)& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{4}{3}q-1x-1.\frac{4}{3}& \text{Uitwerken } \\ & =-qx-\frac{4}{3}q-1x-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-11}{9})(\frac{13}{2}+a)& =(\color{red}{b}+\color{orange}{\frac{-11}{9}}).(\color{green}{a}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{2}b-\frac{11}{9}a-\frac{11}{9}.\frac{13}{2}& \text{Uitwerken } \\ & =ab+\frac{13}{2}b-\frac{11}{9}a-\frac{143}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-4}{13})(b+\frac{-6}{4})& =(\color{red}{x}+\color{orange}{\frac{-4}{13}}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{2}x-\frac{4}{13}b+\frac{4}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =bx-\frac{3}{2}x-\frac{4}{13}b+\frac{12}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{3}{2}x-\frac{4}{13}b+\frac{6}{13} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p+\frac{13}{14})(p-\frac{-13}{8})& =(\color{red}{p}+\color{orange}{\frac{13}{14}}).(\color{green}{p}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{13}{14})} . \color{green}{(p)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{13}{8}p+\frac{13}{14}p+\frac{13}{14}.\frac{13}{8}& \text{Uitwerken } \\ & =p^2+(\frac{13}{8}+\frac{13}{14})p+\frac{169}{112} & \text{Neem samen} \\ &=p^2+\frac{143}{56}p+\frac{169}{112} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-12}{2})(\frac{-14}{19}+b)& =(\color{red}{b}+\color{orange}{6}).(\color{green}{b}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(6)} . \color{green}{(b)} + \color{orange}{(6)} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{14}{19}b+6b-6.\frac{14}{19}& \text{Uitwerken } \\ & =b^2+((\frac{-14}{19})+6)b-(\frac{-84}{19}) & \text{Neem samen} \\ &=b^2+\frac{100}{19}b-(\frac{-84}{19}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{4}{13}+p)(a-\frac{-18}{18})& =(\color{red}{p}+\color{orange}{\frac{4}{13}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{4}{13})} . \color{green}{(a)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1p+\frac{4}{13}a+\frac{4}{13}.1& \text{Uitwerken } \\ & =ap+1p+\frac{4}{13}a+\frac{4}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-6}{12}-x)(\frac{-14}{17}+p)& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{14}{17}x-\frac{1}{2}p+\frac{1}{2}.\frac{14}{17}& \text{Uitwerken } \\ & =-px+\frac{14}{17}x-\frac{1}{2}p+\frac{14}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{14}{17}x-\frac{1}{2}p+\frac{7}{17} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-18}{16})(\frac{8}{14}-b)& =(\color{red}{x}+\color{orange}{\frac{-9}{8}}).(\color{green}{-b}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{4}{7}x+\frac{9}{8}b-\frac{9}{8}.\frac{4}{7}& \text{Uitwerken } \\ & =-bx+\frac{4}{7}x+\frac{9}{8}b-\frac{36}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{4}{7}x+\frac{9}{8}b-\frac{9}{14} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-2}{6}+a)(\frac{17}{3}+a)& =(\color{red}{a}+\color{orange}{\frac{-1}{3}}).(\color{green}{a}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{17}{3}a-\frac{1}{3}a-\frac{1}{3}.\frac{17}{3}& \text{Uitwerken } \\ & =a^2+(\frac{17}{3}+(\frac{-1}{3}))a-(\frac{-17}{9}) & \text{Neem samen} \\ &=a^2+\frac{16}{3}a-(\frac{-17}{9}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{8}{8}-p)(a+\frac{-5}{9})& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{9}p+1a-1.\frac{5}{9}& \text{Uitwerken } \\ & =-ap+\frac{5}{9}p+1a-\frac{5}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-18}{3})(x+\frac{9}{4})& =(\color{red}{p}+\color{orange}{6}).(\color{green}{x}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(6)} . \color{green}{(x)} + \color{orange}{(6)} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{4}p+6x+6.\frac{9}{4}& \text{Uitwerken } \\ & =px+\frac{9}{4}p+6x+\frac{54}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{9}{4}p+6x+\frac{27}{2} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{16}{11}-a)(\frac{19}{9}-p)& =(\color{red}{-a}+\color{orange}{\frac{16}{11}}).(\color{green}{-p}+\color{blue}{\frac{19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{9})} + \color{orange}{(\frac{16}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{19}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{9}a-\frac{16}{11}p+\frac{16}{11}.\frac{19}{9}& \text{Uitwerken } \\ & =ap-\frac{19}{9}a-\frac{16}{11}p+\frac{304}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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