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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-6}{7}+q)(a+\frac{1}{3})& =(\color{red}{q}+\color{orange}{\frac{-6}{7}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{3}q-\frac{6}{7}a-\frac{6}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =aq+\frac{1}{3}q-\frac{6}{7}a-\frac{6}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{1}{3}q-\frac{6}{7}a-\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-14}{7})(p-\frac{15}{7})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{15}{7}p-2p+2.\frac{15}{7}& \text{Uitwerken } \\ & =p^2+((\frac{-15}{7})+(-2))p+\frac{30}{7} & \text{Neem samen} \\ &=p^2-\frac{29}{7}p+\frac{30}{7} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(p-\frac{8}{7})(p+\frac{-6}{17})& =(\color{red}{p}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{6}{17}p-\frac{8}{7}p+\frac{8}{7}.\frac{6}{17}& \text{Uitwerken } \\ & =p^2+((\frac{-6}{17})+(\frac{-8}{7}))p+\frac{48}{119} & \text{Neem samen} \\ &=p^2-\frac{178}{119}p+\frac{48}{119} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(p-\frac{19}{5})(a-\frac{19}{12})& =(\color{red}{p}+\color{orange}{\frac{-19}{5}}).(\color{green}{a}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{12}p-\frac{19}{5}a+\frac{19}{5}.\frac{19}{12}& \text{Uitwerken } \\ & =ap-\frac{19}{12}p-\frac{19}{5}a+\frac{361}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{8}-a)(\frac{-5}{9}-a)& =(\color{red}{-a}+\color{orange}{\frac{-15}{8}}).(\color{green}{-a}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{9}a+\frac{15}{8}a+\frac{15}{8}.\frac{5}{9}& \text{Uitwerken } \\ & =a^2+(\frac{5}{9}+\frac{15}{8})a+\frac{75}{72} & \text{Neem samen} \\ &=a^2+\frac{175}{72}a+\frac{75}{72} & \text{Maak de som} \\ &=a^2+\frac{175}{72}a+\frac{25}{24} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{11}{3}+a)(\frac{2}{3}+p)& =(\color{red}{a}+\color{orange}{\frac{11}{3}}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{11}{3})} . \color{green}{(p)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{3}a+\frac{11}{3}p+\frac{11}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =ap+\frac{2}{3}a+\frac{11}{3}p+\frac{22}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-18}{2}-q)(b-\frac{2}{19})& =(\color{red}{-q}+\color{orange}{(-9)}).(\color{green}{b}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(-9)} . \color{green}{(b)} + \color{orange}{(-9)} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{19}q-9b+9.\frac{2}{19}& \text{Uitwerken } \\ & =-bq+\frac{2}{19}q-9b+\frac{18}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{14}{6}-b)(\frac{-19}{19}+q)& =(\color{red}{-b}+\color{orange}{\frac{7}{3}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(\frac{7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bq+1b+\frac{7}{3}q-\frac{7}{3}.1& \text{Uitwerken } \\ & =-bq+1b+\frac{7}{3}q-\frac{7}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-15}{11})(\frac{-17}{15}+b)& =(\color{red}{a}+\color{orange}{\frac{15}{11}}).(\color{green}{b}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{15}{11})} . \color{green}{(b)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{17}{15}a+\frac{15}{11}b-\frac{15}{11}.\frac{17}{15}& \text{Uitwerken } \\ & =ab-\frac{17}{15}a+\frac{15}{11}b-\frac{255}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{17}{15}a+\frac{15}{11}b-\frac{17}{11} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{7}{9}+a)(\frac{-3}{15}+p)& =(\color{red}{a}+\color{orange}{\frac{7}{9}}).(\color{green}{p}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{7}{9})} . \color{green}{(p)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{5}a+\frac{7}{9}p-\frac{7}{9}.\frac{1}{5}& \text{Uitwerken } \\ & =ap-\frac{1}{5}a+\frac{7}{9}p-\frac{7}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{11}{14})(q-\frac{-17}{3})& =(\color{red}{b}+\color{orange}{\frac{-11}{14}}).(\color{green}{q}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{3}b-\frac{11}{14}q-\frac{11}{14}.\frac{17}{3}& \text{Uitwerken } \\ & =bq+\frac{17}{3}b-\frac{11}{14}q-\frac{187}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{17}{18}-b)(\frac{9}{3}-p)& =(\color{red}{-b}+\color{orange}{\frac{17}{18}}).(\color{green}{-p}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(3)} + \color{orange}{(\frac{17}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bp-3b-\frac{17}{18}p+\frac{17}{18}.3& \text{Uitwerken } \\ & =bp-3b-\frac{17}{18}p+\frac{51}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-3b-\frac{17}{18}p+\frac{17}{6} & \text{Vereenvoudig} \\\end{align}\)
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