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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{4}{12})(b+\frac{15}{4})& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{15}{4}b-\frac{1}{3}b-\frac{1}{3}.\frac{15}{4}& \text{Uitwerken } \\ & =b^2+(\frac{15}{4}+(\frac{-1}{3}))b-(\frac{-15}{12}) & \text{Neem samen} \\ &=b^2+\frac{41}{12}b-(\frac{-15}{12}) & \text{Maak de som} \\ &=b^2+\frac{41}{12}b+\frac{5}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(\frac{-7}{2}+q)(b-\frac{-5}{6})& =(\color{red}{q}+\color{orange}{\frac{-7}{2}}).(\color{green}{b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{6}q-\frac{7}{2}b-\frac{7}{2}.\frac{5}{6}& \text{Uitwerken } \\ & =bq+\frac{5}{6}q-\frac{7}{2}b-\frac{35}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{14}{19})(\frac{11}{13}-p)& =(\color{red}{q}+\color{orange}{\frac{14}{19}}).(\color{green}{-p}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{14}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{13}q-\frac{14}{19}p+\frac{14}{19}.\frac{11}{13}& \text{Uitwerken } \\ & =-pq+\frac{11}{13}q-\frac{14}{19}p+\frac{154}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-8}{3}-q)(\frac{18}{17}-p)& =(\color{red}{-q}+\color{orange}{\frac{-8}{3}}).(\color{green}{-p}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{18}{17}q+\frac{8}{3}p-\frac{8}{3}.\frac{18}{17}& \text{Uitwerken } \\ & =pq-\frac{18}{17}q+\frac{8}{3}p-\frac{144}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{18}{17}q+\frac{8}{3}p-\frac{48}{17} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-18}{8})(\frac{11}{5}+a)& =(\color{red}{a}+\color{orange}{\frac{-9}{4}}).(\color{green}{a}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{11}{5}a-\frac{9}{4}a-\frac{9}{4}.\frac{11}{5}& \text{Uitwerken } \\ & =a^2+(\frac{11}{5}+(\frac{-9}{4}))a-(\frac{-99}{20}) & \text{Neem samen} \\ &=a^2-\frac{1}{20}a-(\frac{-99}{20}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(q+\frac{19}{4})(\frac{-13}{3}+a)& =(\color{red}{q}+\color{orange}{\frac{19}{4}}).(\color{green}{a}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{19}{4})} . \color{green}{(a)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{3}q+\frac{19}{4}a-\frac{19}{4}.\frac{13}{3}& \text{Uitwerken } \\ & =aq-\frac{13}{3}q+\frac{19}{4}a-\frac{247}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{17}-q)(\frac{4}{18}+x)& =(\color{red}{-q}+\color{orange}{\frac{9}{17}}).(\color{green}{x}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{9}{17})} . \color{green}{(x)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{9}q+\frac{9}{17}x+\frac{9}{17}.\frac{2}{9}& \text{Uitwerken } \\ & =-qx-\frac{2}{9}q+\frac{9}{17}x+\frac{18}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{2}{9}q+\frac{9}{17}x+\frac{2}{17} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{10}{8}-x)(\frac{-12}{17}-x)& =(\color{red}{-x}+\color{orange}{\frac{5}{4}}).(\color{green}{-x}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{12}{17}x-\frac{5}{4}x-\frac{5}{4}.\frac{12}{17}& \text{Uitwerken } \\ & =x^2+(\frac{12}{17}+(\frac{-5}{4}))x-(\frac{-60}{68}) & \text{Neem samen} \\ &=x^2-\frac{37}{68}x-(\frac{-60}{68}) & \text{Maak de som} \\ &=x^2-\frac{37}{68}x+\frac{15}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{14}{6}+p)(4-p)& =(\color{red}{p}+\color{orange}{\frac{7}{3}}).(\color{green}{-p}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{7}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -pp+4p-\frac{7}{3}p+\frac{7}{3}.4& \text{Uitwerken } \\ & =-p^2+(4+(\frac{-7}{3}))p+(\frac{-28}{3}) & \text{Neem samen} \\ &=-p^2+\frac{5}{3}p+(\frac{-28}{3}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-7}{11})(q-\frac{11}{9})& =(\color{red}{a}+\color{orange}{\frac{-7}{11}}).(\color{green}{q}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{9}a-\frac{7}{11}q+\frac{7}{11}.\frac{11}{9}& \text{Uitwerken } \\ & =aq-\frac{11}{9}a-\frac{7}{11}q+\frac{77}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{11}{9}a-\frac{7}{11}q+\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{4}+x)(x+\frac{-17}{2})& =(\color{red}{x}+\color{orange}{\frac{7}{2}}).(\color{green}{x}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{17}{2}x+\frac{7}{2}x-\frac{7}{2}.\frac{17}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-17}{2})+\frac{7}{2})x-(\frac{-119}{4}) & \text{Neem samen} \\ &=x^2-\frac{10}{2}x-(\frac{-119}{4}) & \text{Maak de som} \\ &=x^2-5x+\frac{119}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{-14}{12}+p)(p+\frac{-18}{15})& =(\color{red}{p}+\color{orange}{\frac{-7}{6}}).(\color{green}{p}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{6}{5}p-\frac{7}{6}p+\frac{7}{6}.\frac{6}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-6}{5})+(\frac{-7}{6}))p+\frac{42}{30} & \text{Neem samen} \\ &=p^2-\frac{71}{30}p+\frac{42}{30} & \text{Maak de som} \\ &=p^2-\frac{71}{30}p+\frac{7}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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