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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-11}{17})(x-\frac{-4}{4})& =(\color{red}{b}+\color{orange}{\frac{-11}{17}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-11}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1b-\frac{11}{17}x-\frac{11}{17}.1& \text{Uitwerken } \\ & =bx+1b-\frac{11}{17}x-\frac{11}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-2}{14})(\frac{-10}{18}+a)& =(\color{red}{a}+\color{orange}{\frac{-1}{7}}).(\color{green}{a}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{9}a-\frac{1}{7}a+\frac{1}{7}.\frac{5}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{9})+(\frac{-1}{7}))a+\frac{5}{63} & \text{Neem samen} \\ &=a^2-\frac{44}{63}a+\frac{5}{63} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{15}{6}-q)(\frac{-1}{7}-a)& =(\color{red}{-q}+\color{orange}{\frac{5}{2}}).(\color{green}{-a}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{7}q-\frac{5}{2}a-\frac{5}{2}.\frac{1}{7}& \text{Uitwerken } \\ & =aq+\frac{1}{7}q-\frac{5}{2}a-\frac{5}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-19}{20})(\frac{16}{14}-a)& =(\color{red}{p}+\color{orange}{\frac{-19}{20}}).(\color{green}{-a}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{8}{7}p+\frac{19}{20}a-\frac{19}{20}.\frac{8}{7}& \text{Uitwerken } \\ & =-ap+\frac{8}{7}p+\frac{19}{20}a-\frac{152}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{8}{7}p+\frac{19}{20}a-\frac{38}{35} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{3}+a)(b-\frac{15}{18})& =(\color{red}{a}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{6}a+3b-3.\frac{5}{6}& \text{Uitwerken } \\ & =ab-\frac{5}{6}a+3b-\frac{15}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{6}a+3b-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-9}{11})(\frac{-9}{14}-b)& =(\color{red}{x}+\color{orange}{\frac{-9}{11}}).(\color{green}{-b}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{9}{14}x+\frac{9}{11}b+\frac{9}{11}.\frac{9}{14}& \text{Uitwerken } \\ & =-bx-\frac{9}{14}x+\frac{9}{11}b+\frac{81}{154} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{2}+b)(\frac{4}{17}-q)& =(\color{red}{b}+\color{orange}{4}).(\color{green}{-q}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(4)} . \color{green}{(-q)} + \color{orange}{(4)} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{4}{17}b-4q+4.\frac{4}{17}& \text{Uitwerken } \\ & =-bq+\frac{4}{17}b-4q+\frac{16}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{19}{12})(a+\frac{-7}{12})& =(\color{red}{a}+\color{orange}{\frac{-19}{12}}).(\color{green}{a}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{7}{12}a-\frac{19}{12}a+\frac{19}{12}.\frac{7}{12}& \text{Uitwerken } \\ & =a^2+((\frac{-7}{12})+(\frac{-19}{12}))a+\frac{133}{144} & \text{Neem samen} \\ &=a^2-\frac{26}{12}a+\frac{133}{144} & \text{Maak de som} \\ &=a^2-\frac{13}{6}a+\frac{133}{144} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-20}{13}+q)(\frac{-1}{11}+x)& =(\color{red}{q}+\color{orange}{\frac{-20}{13}}).(\color{green}{x}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{11}q-\frac{20}{13}x+\frac{20}{13}.\frac{1}{11}& \text{Uitwerken } \\ & =qx-\frac{1}{11}q-\frac{20}{13}x+\frac{20}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{6}{16}+p)(\frac{5}{7}+a)& =(\color{red}{p}+\color{orange}{\frac{3}{8}}).(\color{green}{a}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{3}{8})} . \color{green}{(a)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{7}p+\frac{3}{8}a+\frac{3}{8}.\frac{5}{7}& \text{Uitwerken } \\ & =ap+\frac{5}{7}p+\frac{3}{8}a+\frac{15}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-3}{11}-x)(19+p)& =(\color{red}{-x}+\color{orange}{\frac{-3}{11}}).(\color{green}{p}+\color{blue}{19})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(19)} + \color{orange}{(\frac{-3}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = -px-19x-\frac{3}{11}p-\frac{3}{11}.19& \text{Uitwerken } \\ & =-px-19x-\frac{3}{11}p-\frac{57}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{13}{8})(a-\frac{11}{3})& =(\color{red}{a}+\color{orange}{\frac{13}{8}}).(\color{green}{a}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{13}{8})} . \color{green}{(a)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{11}{3}a+\frac{13}{8}a-\frac{13}{8}.\frac{11}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-11}{3})+\frac{13}{8})a-(\frac{-143}{24}) & \text{Neem samen} \\ &=a^2-\frac{49}{24}a-(\frac{-143}{24}) & \text{Maak de som} \\\end{align}\)
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