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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{13}{20}-p)(a+\frac{9}{2})& =(\color{red}{-p}+\color{orange}{\frac{13}{20}}).(\color{green}{a}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{13}{20})} . \color{green}{(a)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{2}p+\frac{13}{20}a+\frac{13}{20}.\frac{9}{2}& \text{Uitwerken } \\ & =-ap-\frac{9}{2}p+\frac{13}{20}a+\frac{117}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{8}{12})(\frac{-4}{17}+x)& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{17}a-\frac{2}{3}x+\frac{2}{3}.\frac{4}{17}& \text{Uitwerken } \\ & =ax-\frac{4}{17}a-\frac{2}{3}x+\frac{8}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-12}{11}-x)(a-\frac{20}{8})& =(\color{red}{-x}+\color{orange}{\frac{-12}{11}}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{2}x-\frac{12}{11}a+\frac{12}{11}.\frac{5}{2}& \text{Uitwerken } \\ & =-ax+\frac{5}{2}x-\frac{12}{11}a+\frac{60}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{5}{2}x-\frac{12}{11}a+\frac{30}{11} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-13}{14}+b)(\frac{2}{4}+x)& =(\color{red}{b}+\color{orange}{\frac{-13}{14}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}b-\frac{13}{14}x-\frac{13}{14}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}b-\frac{13}{14}x-\frac{13}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{14}{4})(\frac{-18}{4}-b)& =(\color{red}{b}+\color{orange}{\frac{-7}{2}}).(\color{green}{-b}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{9}{2}b+\frac{7}{2}b+\frac{7}{2}.\frac{9}{2}& \text{Uitwerken } \\ & =-b^2+((\frac{-9}{2})+\frac{7}{2})b+(\frac{-63}{4}) & \text{Neem samen} \\ &=-b^2-\frac{2}{2}b+(\frac{-63}{4}) & \text{Maak de som} \\ &=-b^2-1b+(\frac{-63}{4}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{-2}{2}-a)(\frac{-16}{14}-x)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{8}{7}a+1x+1.\frac{8}{7}& \text{Uitwerken } \\ & =ax+\frac{8}{7}a+1x+\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-20}{9}-x)(q-\frac{-18}{17})& =(\color{red}{-x}+\color{orange}{\frac{-20}{9}}).(\color{green}{q}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{-20}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{18}{17}x-\frac{20}{9}q-\frac{20}{9}.\frac{18}{17}& \text{Uitwerken } \\ & =-qx-\frac{18}{17}x-\frac{20}{9}q-\frac{360}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{18}{17}x-\frac{20}{9}q-\frac{40}{17} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-15}{18}-q)(\frac{-7}{13}-q)& =(\color{red}{-q}+\color{orange}{\frac{-5}{6}}).(\color{green}{-q}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{13}q+\frac{5}{6}q+\frac{5}{6}.\frac{7}{13}& \text{Uitwerken } \\ & =q^2+(\frac{7}{13}+\frac{5}{6})q+\frac{35}{78} & \text{Neem samen} \\ &=q^2+\frac{107}{78}q+\frac{35}{78} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-8}{13})(\frac{5}{6}-q)& =(\color{red}{a}+\color{orange}{\frac{8}{13}}).(\color{green}{-q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{8}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{6}a-\frac{8}{13}q+\frac{8}{13}.\frac{5}{6}& \text{Uitwerken } \\ & =-aq+\frac{5}{6}a-\frac{8}{13}q+\frac{40}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{5}{6}a-\frac{8}{13}q+\frac{20}{39} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{17}{11})(\frac{-18}{9}+a)& =(\color{red}{b}+\color{orange}{\frac{-17}{11}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-17}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ab-2b-\frac{17}{11}a+\frac{17}{11}.2& \text{Uitwerken } \\ & =ab-2b-\frac{17}{11}a+\frac{34}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+(-9))(q+\frac{-4}{13})& =(\color{red}{b}+\color{orange}{(-9)}).(\color{green}{q}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(-9)} . \color{green}{(q)} + \color{orange}{(-9)} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{13}b-9q+9.\frac{4}{13}& \text{Uitwerken } \\ & =bq-\frac{4}{13}b-9q+\frac{36}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-6}{2})(\frac{-16}{13}+p)& =(\color{red}{p}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{16}{13}p+3p-3.\frac{16}{13}& \text{Uitwerken } \\ & =p^2+((\frac{-16}{13})+3)p-(\frac{-48}{13}) & \text{Neem samen} \\ &=p^2+\frac{23}{13}p-(\frac{-48}{13}) & \text{Maak de som} \\\end{align}\)
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