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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{8}-a)(\frac{-13}{9}+x)& =(\color{red}{-a}+\color{orange}{\frac{9}{8}}).(\color{green}{x}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{9}a+\frac{9}{8}x-\frac{9}{8}.\frac{13}{9}& \text{Uitwerken } \\ & =-ax+\frac{13}{9}a+\frac{9}{8}x-\frac{117}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{13}{9}a+\frac{9}{8}x-\frac{13}{8} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{9}{11}+x)(\frac{-13}{6}-x)& =(\color{red}{x}+\color{orange}{\frac{9}{11}}).(\color{green}{-x}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{9}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{13}{6}x-\frac{9}{11}x-\frac{9}{11}.\frac{13}{6}& \text{Uitwerken } \\ & =-x^2+((\frac{-13}{6})+(\frac{-9}{11}))x-\frac{117}{66} & \text{Neem samen} \\ &=-x^2-\frac{197}{66}x-\frac{117}{66} & \text{Maak de som} \\ &=-x^2-\frac{197}{66}x-\frac{39}{22} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-19}{11}-q)(a+\frac{-3}{12})& =(\color{red}{-q}+\color{orange}{\frac{-19}{11}}).(\color{green}{a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{4}q-\frac{19}{11}a+\frac{19}{11}.\frac{1}{4}& \text{Uitwerken } \\ & =-aq+\frac{1}{4}q-\frac{19}{11}a+\frac{19}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-17}{17})(\frac{-5}{12}-p)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{5}{12}p+1p+1.\frac{5}{12}& \text{Uitwerken } \\ & =-p^2+((\frac{-5}{12})+1)p+(\frac{-5}{12}) & \text{Neem samen} \\ &=-p^2+\frac{7}{12}p+(\frac{-5}{12}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(q-\frac{9}{5})(a-\frac{12}{3})& =(\color{red}{q}+\color{orange}{\frac{-9}{5}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(\frac{-9}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aq-4q-\frac{9}{5}a+\frac{9}{5}.4& \text{Uitwerken } \\ & =aq-4q-\frac{9}{5}a+\frac{36}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-13}{4}-p)(a-\frac{5}{4})& =(\color{red}{-p}+\color{orange}{\frac{-13}{4}}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{4}p-\frac{13}{4}a+\frac{13}{4}.\frac{5}{4}& \text{Uitwerken } \\ & =-ap+\frac{5}{4}p-\frac{13}{4}a+\frac{65}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{6}+p)(p-\frac{16}{9})& =(\color{red}{p}+\color{orange}{\frac{11}{6}}).(\color{green}{p}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{11}{6})} . \color{green}{(p)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{16}{9}p+\frac{11}{6}p-\frac{11}{6}.\frac{16}{9}& \text{Uitwerken } \\ & =p^2+((\frac{-16}{9})+\frac{11}{6})p-(\frac{-176}{54}) & \text{Neem samen} \\ &=p^2+\frac{1}{18}p-(\frac{-176}{54}) & \text{Maak de som} \\ &=p^2+\frac{1}{18}p+\frac{88}{27} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{12}-q)(b-\frac{-10}{8})& =(\color{red}{-q}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{4}q-\frac{1}{4}b-\frac{1}{4}.\frac{5}{4}& \text{Uitwerken } \\ & =-bq-\frac{5}{4}q-\frac{1}{4}b-\frac{5}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{11}{15})(b-\frac{-15}{20})& =(\color{red}{b}+\color{orange}{\frac{-11}{15}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{4}b-\frac{11}{15}b-\frac{11}{15}.\frac{3}{4}& \text{Uitwerken } \\ & =b^2+(\frac{3}{4}+(\frac{-11}{15}))b-(\frac{-33}{60}) & \text{Neem samen} \\ &=b^2+\frac{1}{60}b-(\frac{-33}{60}) & \text{Maak de som} \\ &=b^2+\frac{1}{60}b+\frac{11}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(a-\frac{13}{10})(q+\frac{20}{18})& =(\color{red}{a}+\color{orange}{\frac{-13}{10}}).(\color{green}{q}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{9}a-\frac{13}{10}q-\frac{13}{10}.\frac{10}{9}& \text{Uitwerken } \\ & =aq+\frac{10}{9}a-\frac{13}{10}q-\frac{130}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{10}{9}a-\frac{13}{10}q-\frac{13}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-10}{3})(x+\frac{-7}{2})& =(\color{red}{q}+\color{orange}{\frac{10}{3}}).(\color{green}{x}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{2}q+\frac{10}{3}x-\frac{10}{3}.\frac{7}{2}& \text{Uitwerken } \\ & =qx-\frac{7}{2}q+\frac{10}{3}x-\frac{70}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{7}{2}q+\frac{10}{3}x-\frac{35}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-3}{11})(\frac{17}{15}+a)& =(\color{red}{b}+\color{orange}{\frac{-3}{11}}).(\color{green}{a}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{15}b-\frac{3}{11}a-\frac{3}{11}.\frac{17}{15}& \text{Uitwerken } \\ & =ab+\frac{17}{15}b-\frac{3}{11}a-\frac{51}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{17}{15}b-\frac{3}{11}a-\frac{17}{55} & \text{Vereenvoudig} \\\end{align}\)
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