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

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

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Verbetersleutel

  1. \(\begin{align}(a+\frac{-19}{11})(\frac{-17}{12}-a)& =(\color{red}{a}+\color{orange}{\frac{-19}{11}}).(\color{green}{-a}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{17}{12}a+\frac{19}{11}a+\frac{19}{11}.\frac{17}{12}& \text{Uitwerken } \\ & =-a^2+((\frac{-17}{12})+\frac{19}{11})a+(\frac{-323}{132}) & \text{Neem samen} \\ &=-a^2+\frac{41}{132}a+(\frac{-323}{132}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{4}{2}+q)(p-\frac{-7}{14})& =(\color{red}{q}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{2}q+2p+2.\frac{1}{2}& \text{Uitwerken } \\ & =pq+\frac{1}{2}q+2p+\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{2}q+2p+1 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{4}+x)(\frac{9}{7}-b)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{-b}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{9}{7}x-\frac{3}{2}b+\frac{3}{2}.\frac{9}{7}& \text{Uitwerken } \\ & =-bx+\frac{9}{7}x-\frac{3}{2}b+\frac{27}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{16}{11}+x)(\frac{-18}{17}+a)& =(\color{red}{x}+\color{orange}{\frac{16}{11}}).(\color{green}{a}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{16}{11})} . \color{green}{(a)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{18}{17}x+\frac{16}{11}a-\frac{16}{11}.\frac{18}{17}& \text{Uitwerken } \\ & =ax-\frac{18}{17}x+\frac{16}{11}a-\frac{288}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-8}{12}+x)(\frac{-11}{4}-a)& =(\color{red}{x}+\color{orange}{\frac{-2}{3}}).(\color{green}{-a}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{4}x+\frac{2}{3}a+\frac{2}{3}.\frac{11}{4}& \text{Uitwerken } \\ & =-ax-\frac{11}{4}x+\frac{2}{3}a+\frac{22}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{11}{4}x+\frac{2}{3}a+\frac{11}{6} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{18}{9}+p)(\frac{5}{14}+p)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{14}p+2p+2.\frac{5}{14}& \text{Uitwerken } \\ & =p^2+(\frac{5}{14}+2)p+\frac{10}{14} & \text{Neem samen} \\ &=p^2+\frac{33}{14}p+\frac{10}{14} & \text{Maak de som} \\ &=p^2+\frac{33}{14}p+\frac{5}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{-2}{3}+q)(a-\frac{11}{9})& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{9}q-\frac{2}{3}a+\frac{2}{3}.\frac{11}{9}& \text{Uitwerken } \\ & =aq-\frac{11}{9}q-\frac{2}{3}a+\frac{22}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{12}-a)(p+\frac{8}{7})& =(\color{red}{-a}+\color{orange}{\frac{-1}{4}}).(\color{green}{p}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{8}{7}a-\frac{1}{4}p-\frac{1}{4}.\frac{8}{7}& \text{Uitwerken } \\ & =-ap-\frac{8}{7}a-\frac{1}{4}p-\frac{8}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{8}{7}a-\frac{1}{4}p-\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-9}{15})(\frac{8}{8}+a)& =(\color{red}{p}+\color{orange}{\frac{-3}{5}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1p-\frac{3}{5}a-\frac{3}{5}.1& \text{Uitwerken } \\ & =ap+1p-\frac{3}{5}a-\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+(-20))(p-\frac{5}{8})& =(\color{red}{a}+\color{orange}{(-20)}).(\color{green}{p}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(-20)} . \color{green}{(p)} + \color{orange}{(-20)} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{8}a-20p+20.\frac{5}{8}& \text{Uitwerken } \\ & =ap-\frac{5}{8}a-20p+\frac{100}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{5}{8}a-20p+\frac{25}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-15}{20}-p)(\frac{13}{14}-x)& =(\color{red}{-p}+\color{orange}{\frac{-3}{4}}).(\color{green}{-x}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{14}p+\frac{3}{4}x-\frac{3}{4}.\frac{13}{14}& \text{Uitwerken } \\ & =px-\frac{13}{14}p+\frac{3}{4}x-\frac{39}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-1}{20}-a)(\frac{-10}{2}+b)& =(\color{red}{-a}+\color{orange}{\frac{-1}{20}}).(\color{green}{b}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(-5)} + \color{orange}{(\frac{-1}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -ab+5a-\frac{1}{20}b+\frac{1}{20}.5& \text{Uitwerken } \\ & =-ab+5a-\frac{1}{20}b+\frac{5}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+5a-\frac{1}{20}b+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
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