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

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  1. \((\frac{13}{5}-q)(\frac{20}{10}-q)\)
  2. \((\frac{8}{18}+p)(b+\frac{-14}{7})\)
  3. \((\frac{19}{14}-b)(\frac{11}{3}-x)\)
  4. \((a+\frac{-18}{19})(\frac{10}{17}+a)\)
  5. \((\frac{-12}{5}-x)(q-\frac{-19}{12})\)
  6. \((\frac{-5}{14}+b)(\frac{3}{17}-p)\)
  7. \((b+\frac{-15}{16})(b-\frac{20}{7})\)
  8. \((\frac{-8}{16}-b)(p-\frac{-20}{3})\)
  9. \((p+\frac{-1}{19})(q-\frac{2}{20})\)
  10. \((\frac{-7}{17}+p)(\frac{13}{18}+x)\)
  11. \((q-\frac{4}{8})(q+\frac{3}{2})\)
  12. \((14+x)(b-\frac{-18}{19})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{13}{5}-q)(\frac{20}{10}-q)& =(\color{red}{-q}+\color{orange}{\frac{13}{5}}).(\color{green}{-q}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{13}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qq-2q-\frac{13}{5}q+\frac{13}{5}.2& \text{Uitwerken } \\ & =q^2+((-2)+(\frac{-13}{5}))q+\frac{26}{5} & \text{Neem samen} \\ &=q^2-\frac{23}{5}q+\frac{26}{5} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{18}+p)(b+\frac{-14}{7})& =(\color{red}{p}+\color{orange}{\frac{4}{9}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bp-2p+\frac{4}{9}b-\frac{4}{9}.2& \text{Uitwerken } \\ & =bp-2p+\frac{4}{9}b-\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{19}{14}-b)(\frac{11}{3}-x)& =(\color{red}{-b}+\color{orange}{\frac{19}{14}}).(\color{green}{-x}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{19}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{3}b-\frac{19}{14}x+\frac{19}{14}.\frac{11}{3}& \text{Uitwerken } \\ & =bx-\frac{11}{3}b-\frac{19}{14}x+\frac{209}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-18}{19})(\frac{10}{17}+a)& =(\color{red}{a}+\color{orange}{\frac{-18}{19}}).(\color{green}{a}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{10}{17}a-\frac{18}{19}a-\frac{18}{19}.\frac{10}{17}& \text{Uitwerken } \\ & =a^2+(\frac{10}{17}+(\frac{-18}{19}))a-(\frac{-180}{323}) & \text{Neem samen} \\ &=a^2-\frac{116}{323}a-(\frac{-180}{323}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-12}{5}-x)(q-\frac{-19}{12})& =(\color{red}{-x}+\color{orange}{\frac{-12}{5}}).(\color{green}{q}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{-12}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{5})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{12}x-\frac{12}{5}q-\frac{12}{5}.\frac{19}{12}& \text{Uitwerken } \\ & =-qx-\frac{19}{12}x-\frac{12}{5}q-\frac{228}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{19}{12}x-\frac{12}{5}q-\frac{19}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-5}{14}+b)(\frac{3}{17}-p)& =(\color{red}{b}+\color{orange}{\frac{-5}{14}}).(\color{green}{-p}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{3}{17}b+\frac{5}{14}p-\frac{5}{14}.\frac{3}{17}& \text{Uitwerken } \\ & =-bp+\frac{3}{17}b+\frac{5}{14}p-\frac{15}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-15}{16})(b-\frac{20}{7})& =(\color{red}{b}+\color{orange}{\frac{-15}{16}}).(\color{green}{b}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{20}{7}b-\frac{15}{16}b+\frac{15}{16}.\frac{20}{7}& \text{Uitwerken } \\ & =b^2+((\frac{-20}{7})+(\frac{-15}{16}))b+\frac{300}{112} & \text{Neem samen} \\ &=b^2-\frac{425}{112}b+\frac{300}{112} & \text{Maak de som} \\ &=b^2-\frac{425}{112}b+\frac{75}{28} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-8}{16}-b)(p-\frac{-20}{3})& =(\color{red}{-b}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{20}{3}b-\frac{1}{2}p-\frac{1}{2}.\frac{20}{3}& \text{Uitwerken } \\ & =-bp-\frac{20}{3}b-\frac{1}{2}p-\frac{20}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{20}{3}b-\frac{1}{2}p-\frac{10}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-1}{19})(q-\frac{2}{20})& =(\color{red}{p}+\color{orange}{\frac{-1}{19}}).(\color{green}{q}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-1}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{10}p-\frac{1}{19}q+\frac{1}{19}.\frac{1}{10}& \text{Uitwerken } \\ & =pq-\frac{1}{10}p-\frac{1}{19}q+\frac{1}{190} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-7}{17}+p)(\frac{13}{18}+x)& =(\color{red}{p}+\color{orange}{\frac{-7}{17}}).(\color{green}{x}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{18}p-\frac{7}{17}x-\frac{7}{17}.\frac{13}{18}& \text{Uitwerken } \\ & =px+\frac{13}{18}p-\frac{7}{17}x-\frac{91}{306} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{4}{8})(q+\frac{3}{2})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{2}q-\frac{1}{2}q-\frac{1}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =q^2+(\frac{3}{2}+(\frac{-1}{2}))q-(\frac{-3}{4}) & \text{Neem samen} \\ &=q^2+\frac{2}{2}q-(\frac{-3}{4}) & \text{Maak de som} \\ &=q^2+1q+\frac{3}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(14+x)(b-\frac{-18}{19})& =(\color{red}{x}+\color{orange}{14}).(\color{green}{b}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(14)} . \color{green}{(b)} + \color{orange}{(14)} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{18}{19}x+14b+14.\frac{18}{19}& \text{Uitwerken } \\ & =bx+\frac{18}{19}x+14b+\frac{252}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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