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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{4}{10})(x+\frac{-8}{7})& =(\color{red}{q}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{8}{7}q+\frac{2}{5}x-\frac{2}{5}.\frac{8}{7}& \text{Uitwerken } \\ & =qx-\frac{8}{7}q+\frac{2}{5}x-\frac{16}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{11}{19}+q)(a-\frac{-6}{17})& =(\color{red}{q}+\color{orange}{\frac{11}{19}}).(\color{green}{a}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{11}{19})} . \color{green}{(a)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{17}q+\frac{11}{19}a+\frac{11}{19}.\frac{6}{17}& \text{Uitwerken } \\ & =aq+\frac{6}{17}q+\frac{11}{19}a+\frac{66}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{16}{4})(\frac{9}{16}+p)& =(\color{red}{p}+\color{orange}{4}).(\color{green}{p}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{16}p+4p+4.\frac{9}{16}& \text{Uitwerken } \\ & =p^2+(\frac{9}{16}+4)p+\frac{36}{16} & \text{Neem samen} \\ &=p^2+\frac{73}{16}p+\frac{36}{16} & \text{Maak de som} \\ &=p^2+\frac{73}{16}p+\frac{9}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{-9}{17}-q)(\frac{11}{10}-p)& =(\color{red}{-q}+\color{orange}{\frac{-9}{17}}).(\color{green}{-p}+\color{blue}{\frac{11}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{10})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{11}{10})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{10}q+\frac{9}{17}p-\frac{9}{17}.\frac{11}{10}& \text{Uitwerken } \\ & =pq-\frac{11}{10}q+\frac{9}{17}p-\frac{99}{170} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{8}{11}+q)(x-\frac{1}{7})& =(\color{red}{q}+\color{orange}{\frac{8}{11}}).(\color{green}{x}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{8}{11})} . \color{green}{(x)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{7}q+\frac{8}{11}x-\frac{8}{11}.\frac{1}{7}& \text{Uitwerken } \\ & =qx-\frac{1}{7}q+\frac{8}{11}x-\frac{8}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{16}{5})(\frac{9}{17}-q)& =(\color{red}{p}+\color{orange}{\frac{-16}{5}}).(\color{green}{-q}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{17}p+\frac{16}{5}q-\frac{16}{5}.\frac{9}{17}& \text{Uitwerken } \\ & =-pq+\frac{9}{17}p+\frac{16}{5}q-\frac{144}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-10}{3})(b+\frac{-3}{11})& =(\color{red}{a}+\color{orange}{\frac{10}{3}}).(\color{green}{b}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{10}{3})} . \color{green}{(b)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{11}a+\frac{10}{3}b-\frac{10}{3}.\frac{3}{11}& \text{Uitwerken } \\ & =ab-\frac{3}{11}a+\frac{10}{3}b-\frac{30}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{3}{11}a+\frac{10}{3}b-\frac{10}{11} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{19}{19}+q)(\frac{-9}{8}-q)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{9}{8}q-1q-1.\frac{9}{8}& \text{Uitwerken } \\ & =-q^2+((\frac{-9}{8})+(-1))q-\frac{9}{8} & \text{Neem samen} \\ &=-q^2-\frac{17}{8}q-\frac{9}{8} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(q+\frac{15}{18})(p+\frac{16}{18})& =(\color{red}{q}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{9}q+\frac{5}{6}p+\frac{5}{6}.\frac{8}{9}& \text{Uitwerken } \\ & =pq+\frac{8}{9}q+\frac{5}{6}p+\frac{40}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{8}{9}q+\frac{5}{6}p+\frac{20}{27} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{12}{10})(q+\frac{9}{11})& =(\color{red}{p}+\color{orange}{\frac{-6}{5}}).(\color{green}{q}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{11}p-\frac{6}{5}q-\frac{6}{5}.\frac{9}{11}& \text{Uitwerken } \\ & =pq+\frac{9}{11}p-\frac{6}{5}q-\frac{54}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{9}{8}-p)(\frac{6}{20}+p)& =(\color{red}{-p}+\color{orange}{\frac{9}{8}}).(\color{green}{p}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{9}{8})} . \color{green}{(p)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{3}{10}p+\frac{9}{8}p+\frac{9}{8}.\frac{3}{10}& \text{Uitwerken } \\ & =-p^2+((\frac{-3}{10})+\frac{9}{8})p+(\frac{-27}{80}) & \text{Neem samen} \\ &=-p^2+\frac{33}{40}p+(\frac{-27}{80}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-14}{8}-a)(\frac{16}{14}+b)& =(\color{red}{-a}+\color{orange}{\frac{-7}{4}}).(\color{green}{b}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{8}{7}a-\frac{7}{4}b-\frac{7}{4}.\frac{8}{7}& \text{Uitwerken } \\ & =-ab-\frac{8}{7}a-\frac{7}{4}b-\frac{56}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{8}{7}a-\frac{7}{4}b-2 & \text{Vereenvoudig} \\\end{align}\)
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