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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{2}-a)(\frac{11}{6}-p)& =(\color{red}{-a}+\color{orange}{\frac{-19}{2}}).(\color{green}{-p}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{6}a+\frac{19}{2}p-\frac{19}{2}.\frac{11}{6}& \text{Uitwerken } \\ & =ap-\frac{11}{6}a+\frac{19}{2}p-\frac{209}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-16}{9})(x-\frac{19}{14})& =(\color{red}{q}+\color{orange}{\frac{16}{9}}).(\color{green}{x}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{16}{9})} . \color{green}{(x)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{14}q+\frac{16}{9}x-\frac{16}{9}.\frac{19}{14}& \text{Uitwerken } \\ & =qx-\frac{19}{14}q+\frac{16}{9}x-\frac{304}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{19}{14}q+\frac{16}{9}x-\frac{152}{63} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-17}{2})(a-\frac{-8}{15})& =(\color{red}{x}+\color{orange}{\frac{17}{2}}).(\color{green}{a}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(\frac{17}{2})} . \color{green}{(a)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{8}{15}x+\frac{17}{2}a+\frac{17}{2}.\frac{8}{15}& \text{Uitwerken } \\ & =ax+\frac{8}{15}x+\frac{17}{2}a+\frac{136}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{8}{15}x+\frac{17}{2}a+\frac{68}{15} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-19}{17})(3+p)& =(\color{red}{q}+\color{orange}{\frac{-19}{17}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{-19}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = pq+3q-\frac{19}{17}p-\frac{19}{17}.3& \text{Uitwerken } \\ & =pq+3q-\frac{19}{17}p-\frac{57}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{17}-x)(x+\frac{6}{2})& =(\color{red}{-x}+\color{orange}{\frac{-6}{17}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(3)} + \color{orange}{(\frac{-6}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -xx-3x-\frac{6}{17}x-\frac{6}{17}.3& \text{Uitwerken } \\ & =-x^2+((-3)+(\frac{-6}{17}))x-\frac{18}{17} & \text{Neem samen} \\ &=-x^2-\frac{57}{17}x-\frac{18}{17} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-8}{7})(p+16)& =(\color{red}{p}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{16})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(16)} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = pp+16p-\frac{8}{7}p-\frac{8}{7}.16& \text{Uitwerken } \\ & =p^2+(16+(\frac{-8}{7}))p-(\frac{-128}{7}) & \text{Neem samen} \\ &=p^2+\frac{104}{7}p-(\frac{-128}{7}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-5}{12}-a)(q-\frac{-13}{4})& =(\color{red}{-a}+\color{orange}{\frac{-5}{12}}).(\color{green}{q}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-5}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{12})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{13}{4}a-\frac{5}{12}q-\frac{5}{12}.\frac{13}{4}& \text{Uitwerken } \\ & =-aq-\frac{13}{4}a-\frac{5}{12}q-\frac{65}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-9}{4})(\frac{-10}{5}+q)& =(\color{red}{a}+\color{orange}{\frac{9}{4}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{9}{4})} . \color{green}{(q)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aq-2a+\frac{9}{4}q-\frac{9}{4}.2& \text{Uitwerken } \\ & =aq-2a+\frac{9}{4}q-\frac{18}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-2a+\frac{9}{4}q-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-6}{14}+p)(b+\frac{13}{20})& =(\color{red}{p}+\color{orange}{\frac{-3}{7}}).(\color{green}{b}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{20}p-\frac{3}{7}b-\frac{3}{7}.\frac{13}{20}& \text{Uitwerken } \\ & =bp+\frac{13}{20}p-\frac{3}{7}b-\frac{39}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{20}{14}+q)(q+\frac{-1}{14})& =(\color{red}{q}+\color{orange}{\frac{10}{7}}).(\color{green}{q}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{10}{7})} . \color{green}{(q)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{14}q+\frac{10}{7}q-\frac{10}{7}.\frac{1}{14}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{14})+\frac{10}{7})q-(\frac{-10}{98}) & \text{Neem samen} \\ &=q^2+\frac{19}{14}q-(\frac{-10}{98}) & \text{Maak de som} \\ &=q^2+\frac{19}{14}q+\frac{5}{49} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(q+\frac{15}{4})(\frac{-1}{8}+q)& =(\color{red}{q}+\color{orange}{\frac{15}{4}}).(\color{green}{q}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{15}{4})} . \color{green}{(q)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{8}q+\frac{15}{4}q-\frac{15}{4}.\frac{1}{8}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{8})+\frac{15}{4})q-(\frac{-15}{32}) & \text{Neem samen} \\ &=q^2+\frac{29}{8}q-(\frac{-15}{32}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-15}{19})(\frac{12}{5}+q)& =(\color{red}{a}+\color{orange}{\frac{15}{19}}).(\color{green}{q}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{15}{19})} . \color{green}{(q)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{12}{5}a+\frac{15}{19}q+\frac{15}{19}.\frac{12}{5}& \text{Uitwerken } \\ & =aq+\frac{12}{5}a+\frac{15}{19}q+\frac{180}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{12}{5}a+\frac{15}{19}q+\frac{36}{19} & \text{Vereenvoudig} \\\end{align}\)
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