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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{9}+x)(a+\frac{3}{17})& =(\color{red}{x}+\color{orange}{\frac{-13}{9}}).(\color{green}{a}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{17}x-\frac{13}{9}a-\frac{13}{9}.\frac{3}{17}& \text{Uitwerken } \\ & =ax+\frac{3}{17}x-\frac{13}{9}a-\frac{39}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{17}x-\frac{13}{9}a-\frac{13}{51} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{7}{20}-p)(p-\frac{-10}{11})& =(\color{red}{-p}+\color{orange}{\frac{7}{20}}).(\color{green}{p}+\color{blue}{\frac{10}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{10}{11})} + \color{orange}{(\frac{7}{20})} . \color{green}{(p)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{10}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{10}{11}p+\frac{7}{20}p+\frac{7}{20}.\frac{10}{11}& \text{Uitwerken } \\ & =-p^2+((\frac{-10}{11})+\frac{7}{20})p+(\frac{-70}{220}) & \text{Neem samen} \\ &=-p^2-\frac{123}{220}p+(\frac{-70}{220}) & \text{Maak de som} \\ &=-p^2-\frac{123}{220}p+(\frac{-7}{22}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{20}{14}+x)(q+\frac{15}{9})& =(\color{red}{x}+\color{orange}{\frac{10}{7}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{10}{7})} . \color{green}{(q)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{3}x+\frac{10}{7}q+\frac{10}{7}.\frac{5}{3}& \text{Uitwerken } \\ & =qx+\frac{5}{3}x+\frac{10}{7}q+\frac{50}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-7}{2}+b)(b+\frac{-7}{18})& =(\color{red}{b}+\color{orange}{\frac{-7}{2}}).(\color{green}{b}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{7}{18}b-\frac{7}{2}b+\frac{7}{2}.\frac{7}{18}& \text{Uitwerken } \\ & =b^2+((\frac{-7}{18})+(\frac{-7}{2}))b+\frac{49}{36} & \text{Neem samen} \\ &=b^2-\frac{70}{18}b+\frac{49}{36} & \text{Maak de som} \\ &=b^2-\frac{35}{9}b+\frac{49}{36} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-5}{14}+b)(q+\frac{17}{6})& =(\color{red}{b}+\color{orange}{\frac{-5}{14}}).(\color{green}{q}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{6}b-\frac{5}{14}q-\frac{5}{14}.\frac{17}{6}& \text{Uitwerken } \\ & =bq+\frac{17}{6}b-\frac{5}{14}q-\frac{85}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{11}{9})(\frac{20}{13}+x)& =(\color{red}{p}+\color{orange}{\frac{-11}{9}}).(\color{green}{x}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{20}{13}p-\frac{11}{9}x-\frac{11}{9}.\frac{20}{13}& \text{Uitwerken } \\ & =px+\frac{20}{13}p-\frac{11}{9}x-\frac{220}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+(-7))(3-b)& =(\color{red}{a}+\color{orange}{(-7)}).(\color{green}{-b}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(-7)} . \color{green}{(-b)} + \color{orange}{(-7)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -ab+3a+7b-7.3& \text{Uitwerken } \\ & =-ab+3a+7b-21 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{1}{18}-a)(\frac{-10}{8}+q)& =(\color{red}{-a}+\color{orange}{\frac{1}{18}}).(\color{green}{q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{1}{18})} . \color{green}{(q)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{4}a+\frac{1}{18}q-\frac{1}{18}.\frac{5}{4}& \text{Uitwerken } \\ & =-aq+\frac{5}{4}a+\frac{1}{18}q-\frac{5}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-(-5))(\frac{-10}{6}+x)& =(\color{red}{a}+\color{orange}{5}).(\color{green}{x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{3}a+5x-5.\frac{5}{3}& \text{Uitwerken } \\ & =ax-\frac{5}{3}a+5x-\frac{25}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{11}{3}+q)(\frac{2}{10}+a)& =(\color{red}{q}+\color{orange}{\frac{11}{3}}).(\color{green}{a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{11}{3})} . \color{green}{(a)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{5}q+\frac{11}{3}a+\frac{11}{3}.\frac{1}{5}& \text{Uitwerken } \\ & =aq+\frac{1}{5}q+\frac{11}{3}a+\frac{11}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{2}{9})(b+\frac{19}{20})& =(\color{red}{p}+\color{orange}{\frac{2}{9}}).(\color{green}{b}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{2}{9})} . \color{green}{(b)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{20}p+\frac{2}{9}b+\frac{2}{9}.\frac{19}{20}& \text{Uitwerken } \\ & =bp+\frac{19}{20}p+\frac{2}{9}b+\frac{38}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{19}{20}p+\frac{2}{9}b+\frac{19}{90} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{9}+b)(\frac{5}{9}-a)& =(\color{red}{b}+\color{orange}{\frac{8}{9}}).(\color{green}{-a}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{8}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{9}b-\frac{8}{9}a+\frac{8}{9}.\frac{5}{9}& \text{Uitwerken } \\ & =-ab+\frac{5}{9}b-\frac{8}{9}a+\frac{40}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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