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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-18}{11})(\frac{3}{17}-p)& =(\color{red}{a}+\color{orange}{\frac{18}{11}}).(\color{green}{-p}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{18}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{17}a-\frac{18}{11}p+\frac{18}{11}.\frac{3}{17}& \text{Uitwerken } \\ & =-ap+\frac{3}{17}a-\frac{18}{11}p+\frac{54}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{15}{9})(\frac{-13}{5}+b)& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{b}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(\frac{5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{13}{5}x+\frac{5}{3}b-\frac{5}{3}.\frac{13}{5}& \text{Uitwerken } \\ & =bx-\frac{13}{5}x+\frac{5}{3}b-\frac{65}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{13}{5}x+\frac{5}{3}b-\frac{13}{3} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{9}{14}-b)(q+\frac{17}{6})& =(\color{red}{-b}+\color{orange}{\frac{9}{14}}).(\color{green}{q}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(\frac{9}{14})} . \color{green}{(q)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{17}{6}b+\frac{9}{14}q+\frac{9}{14}.\frac{17}{6}& \text{Uitwerken } \\ & =-bq-\frac{17}{6}b+\frac{9}{14}q+\frac{153}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{17}{6}b+\frac{9}{14}q+\frac{51}{28} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-9}{7}+b)(\frac{6}{9}+b)& =(\color{red}{b}+\color{orange}{\frac{-9}{7}}).(\color{green}{b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{2}{3}b-\frac{9}{7}b-\frac{9}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =b^2+(\frac{2}{3}+(\frac{-9}{7}))b-(\frac{-18}{21}) & \text{Neem samen} \\ &=b^2-\frac{13}{21}b-(\frac{-18}{21}) & \text{Maak de som} \\ &=b^2-\frac{13}{21}b+\frac{6}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{3}{3}-a)(a-\frac{-4}{20})& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{1}{5}a+1a+1.\frac{1}{5}& \text{Uitwerken } \\ & =-a^2+((\frac{-1}{5})+1)a+(\frac{-1}{5}) & \text{Neem samen} \\ &=-a^2+\frac{4}{5}a+(\frac{-1}{5}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-3}{8})(\frac{-6}{5}+b)& =(\color{red}{a}+\color{orange}{\frac{3}{8}}).(\color{green}{b}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{3}{8})} . \color{green}{(b)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{6}{5}a+\frac{3}{8}b-\frac{3}{8}.\frac{6}{5}& \text{Uitwerken } \\ & =ab-\frac{6}{5}a+\frac{3}{8}b-\frac{18}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{6}{5}a+\frac{3}{8}b-\frac{9}{20} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a+\frac{6}{14})(\frac{-13}{12}-a)& =(\color{red}{a}+\color{orange}{\frac{3}{7}}).(\color{green}{-a}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{3}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{13}{12}a-\frac{3}{7}a-\frac{3}{7}.\frac{13}{12}& \text{Uitwerken } \\ & =-a^2+((\frac{-13}{12})+(\frac{-3}{7}))a-\frac{39}{84} & \text{Neem samen} \\ &=-a^2-\frac{127}{84}a-\frac{39}{84} & \text{Maak de som} \\ &=-a^2-\frac{127}{84}a-\frac{13}{28} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{19}{14}-q)(\frac{4}{10}-x)& =(\color{red}{-q}+\color{orange}{\frac{19}{14}}).(\color{green}{-x}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{19}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{5}q-\frac{19}{14}x+\frac{19}{14}.\frac{2}{5}& \text{Uitwerken } \\ & =qx-\frac{2}{5}q-\frac{19}{14}x+\frac{38}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{2}{5}q-\frac{19}{14}x+\frac{19}{35} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{10}{8}+p)(b-\frac{5}{7})& =(\color{red}{p}+\color{orange}{\frac{5}{4}}).(\color{green}{b}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{7}p+\frac{5}{4}b-\frac{5}{4}.\frac{5}{7}& \text{Uitwerken } \\ & =bp-\frac{5}{7}p+\frac{5}{4}b-\frac{25}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{8}-p)(\frac{2}{5}+p)& =(\color{red}{-p}+\color{orange}{\frac{3}{8}}).(\color{green}{p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{3}{8})} . \color{green}{(p)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{2}{5}p+\frac{3}{8}p+\frac{3}{8}.\frac{2}{5}& \text{Uitwerken } \\ & =-p^2+((\frac{-2}{5})+\frac{3}{8})p+(\frac{-6}{40}) & \text{Neem samen} \\ &=-p^2-\frac{1}{40}p+(\frac{-6}{40}) & \text{Maak de som} \\ &=-p^2-\frac{1}{40}p+(\frac{-3}{20}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{4}+p)(b+\frac{-18}{6})& =(\color{red}{p}+\color{orange}{\frac{7}{2}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bp-3p+\frac{7}{2}b-\frac{7}{2}.3& \text{Uitwerken } \\ & =bp-3p+\frac{7}{2}b-\frac{21}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{11}{2})(\frac{20}{11}-b)& =(\color{red}{x}+\color{orange}{\frac{11}{2}}).(\color{green}{-b}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{11}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{20}{11}x-\frac{11}{2}b+\frac{11}{2}.\frac{20}{11}& \text{Uitwerken } \\ & =-bx+\frac{20}{11}x-\frac{11}{2}b+\frac{220}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{20}{11}x-\frac{11}{2}b+10 & \text{Vereenvoudig} \\\end{align}\)
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