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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{18}{9}+p)(\frac{-15}{17}-q)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{-q}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(2)} . \color{green}{(-q)} + \color{orange}{(2)} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{15}{17}p-2q-2.\frac{15}{17}& \text{Uitwerken } \\ & =-pq-\frac{15}{17}p-2q-\frac{30}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{17}{14}+p)(\frac{-2}{19}+x)& =(\color{red}{p}+\color{orange}{\frac{17}{14}}).(\color{green}{x}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{17}{14})} . \color{green}{(x)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{19}p+\frac{17}{14}x-\frac{17}{14}.\frac{2}{19}& \text{Uitwerken } \\ & =px-\frac{2}{19}p+\frac{17}{14}x-\frac{34}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{2}{19}p+\frac{17}{14}x-\frac{17}{133} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{7}{9})(q-\frac{7}{12})& =(\color{red}{x}+\color{orange}{\frac{-7}{9}}).(\color{green}{q}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{12}x-\frac{7}{9}q+\frac{7}{9}.\frac{7}{12}& \text{Uitwerken } \\ & =qx-\frac{7}{12}x-\frac{7}{9}q+\frac{49}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-19}{12})(a+\frac{-17}{9})& =(\color{red}{a}+\color{orange}{\frac{-19}{12}}).(\color{green}{a}+\color{blue}{\frac{-17}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{9})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-17}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{17}{9}a-\frac{19}{12}a+\frac{19}{12}.\frac{17}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-17}{9})+(\frac{-19}{12}))a+\frac{323}{108} & \text{Neem samen} \\ &=a^2-\frac{125}{36}a+\frac{323}{108} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{20}-p)(x-\frac{-19}{4})& =(\color{red}{-p}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{4}p-\frac{1}{2}x-\frac{1}{2}.\frac{19}{4}& \text{Uitwerken } \\ & =-px-\frac{19}{4}p-\frac{1}{2}x-\frac{19}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-18}{6}+q)(\frac{-9}{14}+a)& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{9}{14}q-3a+3.\frac{9}{14}& \text{Uitwerken } \\ & =aq-\frac{9}{14}q-3a+\frac{27}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-7}{10}+x)(\frac{-15}{2}+x)& =(\color{red}{x}+\color{orange}{\frac{-7}{10}}).(\color{green}{x}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{15}{2}x-\frac{7}{10}x+\frac{7}{10}.\frac{15}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-15}{2})+(\frac{-7}{10}))x+\frac{105}{20} & \text{Neem samen} \\ &=x^2-\frac{82}{10}x+\frac{105}{20} & \text{Maak de som} \\ &=x^2-\frac{41}{5}x+\frac{21}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-11}{19}-b)(q+\frac{-8}{11})& =(\color{red}{-b}+\color{orange}{\frac{-11}{19}}).(\color{green}{q}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{8}{11}b-\frac{11}{19}q+\frac{11}{19}.\frac{8}{11}& \text{Uitwerken } \\ & =-bq+\frac{8}{11}b-\frac{11}{19}q+\frac{88}{209} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{8}{11}b-\frac{11}{19}q+\frac{8}{19} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-5}{8}+p)(\frac{7}{17}+q)& =(\color{red}{p}+\color{orange}{\frac{-5}{8}}).(\color{green}{q}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{17}p-\frac{5}{8}q-\frac{5}{8}.\frac{7}{17}& \text{Uitwerken } \\ & =pq+\frac{7}{17}p-\frac{5}{8}q-\frac{35}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{3}{9})(b+\frac{19}{11})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{11}x+\frac{1}{3}b+\frac{1}{3}.\frac{19}{11}& \text{Uitwerken } \\ & =bx+\frac{19}{11}x+\frac{1}{3}b+\frac{19}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{7}{20})(x-\frac{19}{6})& =(\color{red}{b}+\color{orange}{\frac{-7}{20}}).(\color{green}{x}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{6}b-\frac{7}{20}x+\frac{7}{20}.\frac{19}{6}& \text{Uitwerken } \\ & =bx-\frac{19}{6}b-\frac{7}{20}x+\frac{133}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{1}{8})(\frac{-19}{13}+b)& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{b}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{13}a+\frac{1}{8}b-\frac{1}{8}.\frac{19}{13}& \text{Uitwerken } \\ & =ab-\frac{19}{13}a+\frac{1}{8}b-\frac{19}{104} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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