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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{3}+x)(a-\frac{-13}{9})& =(\color{red}{x}+\color{orange}{\frac{20}{3}}).(\color{green}{a}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{20}{3})} . \color{green}{(a)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{13}{9}x+\frac{20}{3}a+\frac{20}{3}.\frac{13}{9}& \text{Uitwerken } \\ & =ax+\frac{13}{9}x+\frac{20}{3}a+\frac{260}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-15}{17})(\frac{-12}{17}-p)& =(\color{red}{x}+\color{orange}{\frac{15}{17}}).(\color{green}{-p}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{15}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{12}{17}x-\frac{15}{17}p-\frac{15}{17}.\frac{12}{17}& \text{Uitwerken } \\ & =-px-\frac{12}{17}x-\frac{15}{17}p-\frac{180}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-15}{16})(\frac{-11}{7}+q)& =(\color{red}{q}+\color{orange}{\frac{15}{16}}).(\color{green}{q}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{15}{16})} . \color{green}{(q)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{7}q+\frac{15}{16}q-\frac{15}{16}.\frac{11}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{7})+\frac{15}{16})q-(\frac{-165}{112}) & \text{Neem samen} \\ &=q^2-\frac{71}{112}q-(\frac{-165}{112}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(p-\frac{19}{15})(\frac{-16}{3}+p)& =(\color{red}{p}+\color{orange}{\frac{-19}{15}}).(\color{green}{p}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{-19}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{16}{3}p-\frac{19}{15}p+\frac{19}{15}.\frac{16}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-16}{3})+(\frac{-19}{15}))p+\frac{304}{45} & \text{Neem samen} \\ &=p^2-\frac{99}{15}p+\frac{304}{45} & \text{Maak de som} \\ &=p^2-\frac{33}{5}p+\frac{304}{45} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{13}-a)(q+\frac{5}{12})& =(\color{red}{-a}+\color{orange}{\frac{10}{13}}).(\color{green}{q}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{10}{13})} . \color{green}{(q)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{12}a+\frac{10}{13}q+\frac{10}{13}.\frac{5}{12}& \text{Uitwerken } \\ & =-aq-\frac{5}{12}a+\frac{10}{13}q+\frac{50}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{5}{12}a+\frac{10}{13}q+\frac{25}{78} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}((-20)-x)(\frac{-17}{19}-b)& =(\color{red}{-x}+\color{orange}{(-20)}).(\color{green}{-b}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(-20)} . \color{green}{(-b)} + \color{orange}{(-20)} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{19}x+20b+20.\frac{17}{19}& \text{Uitwerken } \\ & =bx+\frac{17}{19}x+20b+\frac{340}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-16}{7}-a)(b+\frac{6}{13})& =(\color{red}{-a}+\color{orange}{\frac{-16}{7}}).(\color{green}{b}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{6}{13}a-\frac{16}{7}b-\frac{16}{7}.\frac{6}{13}& \text{Uitwerken } \\ & =-ab-\frac{6}{13}a-\frac{16}{7}b-\frac{96}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-1}{10}+a)(\frac{9}{7}-p)& =(\color{red}{a}+\color{orange}{\frac{-1}{10}}).(\color{green}{-p}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{7}a+\frac{1}{10}p-\frac{1}{10}.\frac{9}{7}& \text{Uitwerken } \\ & =-ap+\frac{9}{7}a+\frac{1}{10}p-\frac{9}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-11}{19}-a)(\frac{20}{14}-b)& =(\color{red}{-a}+\color{orange}{\frac{-11}{19}}).(\color{green}{-b}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{10}{7}a+\frac{11}{19}b-\frac{11}{19}.\frac{10}{7}& \text{Uitwerken } \\ & =ab-\frac{10}{7}a+\frac{11}{19}b-\frac{110}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-10}{12})(\frac{-16}{13}-b)& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{-b}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{16}{13}q+\frac{5}{6}b+\frac{5}{6}.\frac{16}{13}& \text{Uitwerken } \\ & =-bq-\frac{16}{13}q+\frac{5}{6}b+\frac{80}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{16}{13}q+\frac{5}{6}b+\frac{40}{39} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{11}{17}-q)(\frac{-18}{20}+p)& =(\color{red}{-q}+\color{orange}{\frac{11}{17}}).(\color{green}{p}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{11}{17})} . \color{green}{(p)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{10}q+\frac{11}{17}p-\frac{11}{17}.\frac{9}{10}& \text{Uitwerken } \\ & =-pq+\frac{9}{10}q+\frac{11}{17}p-\frac{99}{170} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{8}+q)(a-\frac{-5}{12})& =(\color{red}{q}+\color{orange}{\frac{-15}{8}}).(\color{green}{a}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{12}q-\frac{15}{8}a-\frac{15}{8}.\frac{5}{12}& \text{Uitwerken } \\ & =aq+\frac{5}{12}q-\frac{15}{8}a-\frac{75}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{5}{12}q-\frac{15}{8}a-\frac{25}{32} & \text{Vereenvoudig} \\\end{align}\)
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