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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-13}{15})(x+\frac{18}{13})& =(\color{red}{a}+\color{orange}{\frac{-13}{15}}).(\color{green}{x}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{18}{13}a-\frac{13}{15}x-\frac{13}{15}.\frac{18}{13}& \text{Uitwerken } \\ & =ax+\frac{18}{13}a-\frac{13}{15}x-\frac{234}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{18}{13}a-\frac{13}{15}x-\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-14}{2}-p)(q-\frac{-9}{16})& =(\color{red}{-p}+\color{orange}{(-7)}).(\color{green}{q}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(-7)} . \color{green}{(q)} + \color{orange}{(-7)} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{16}p-7q-7.\frac{9}{16}& \text{Uitwerken } \\ & =-pq-\frac{9}{16}p-7q-\frac{63}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{18}{16})(\frac{10}{7}-p)& =(\color{red}{x}+\color{orange}{\frac{9}{8}}).(\color{green}{-p}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{9}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{10}{7}x-\frac{9}{8}p+\frac{9}{8}.\frac{10}{7}& \text{Uitwerken } \\ & =-px+\frac{10}{7}x-\frac{9}{8}p+\frac{90}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{10}{7}x-\frac{9}{8}p+\frac{45}{28} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q+\frac{8}{6})(b-\frac{17}{4})& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{4}q+\frac{4}{3}b-\frac{4}{3}.\frac{17}{4}& \text{Uitwerken } \\ & =bq-\frac{17}{4}q+\frac{4}{3}b-\frac{68}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{17}{4}q+\frac{4}{3}b-\frac{17}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{14}{12})(b+\frac{16}{11})& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{b}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{16}{11}a-\frac{7}{6}b-\frac{7}{6}.\frac{16}{11}& \text{Uitwerken } \\ & =ab+\frac{16}{11}a-\frac{7}{6}b-\frac{112}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{16}{11}a-\frac{7}{6}b-\frac{56}{33} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-19}{10}-x)(\frac{-20}{19}-a)& =(\color{red}{-x}+\color{orange}{\frac{-19}{10}}).(\color{green}{-a}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{-19}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{20}{19}x+\frac{19}{10}a+\frac{19}{10}.\frac{20}{19}& \text{Uitwerken } \\ & =ax+\frac{20}{19}x+\frac{19}{10}a+\frac{380}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{20}{19}x+\frac{19}{10}a+2 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{5}-q)(q+\frac{-14}{11})& =(\color{red}{-q}+\color{orange}{\frac{8}{5}}).(\color{green}{q}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{8}{5})} . \color{green}{(q)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{14}{11}q+\frac{8}{5}q-\frac{8}{5}.\frac{14}{11}& \text{Uitwerken } \\ & =-q^2+(\frac{14}{11}+\frac{8}{5})q-\frac{112}{55} & \text{Neem samen} \\ &=-q^2+\frac{158}{55}q-\frac{112}{55} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-3}{7})(x-\frac{-14}{6})& =(\color{red}{b}+\color{orange}{\frac{3}{7}}).(\color{green}{x}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{3}{7})} . \color{green}{(x)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{3}b+\frac{3}{7}x+\frac{3}{7}.\frac{7}{3}& \text{Uitwerken } \\ & =bx+\frac{7}{3}b+\frac{3}{7}x+\frac{21}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{7}{3}b+\frac{3}{7}x+1 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{10}{15}-x)(x+\frac{20}{8})& =(\color{red}{-x}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{5}{2}x+\frac{2}{3}x+\frac{2}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =-x^2+((\frac{-5}{2})+\frac{2}{3})x+(\frac{-10}{6}) & \text{Neem samen} \\ &=-x^2-\frac{11}{6}x+(\frac{-10}{6}) & \text{Maak de som} \\ &=-x^2-\frac{11}{6}x+(\frac{-5}{3}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-13}{5})(\frac{18}{4}-x)& =(\color{red}{a}+\color{orange}{\frac{-13}{5}}).(\color{green}{-x}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-13}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{5})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{2}a+\frac{13}{5}x-\frac{13}{5}.\frac{9}{2}& \text{Uitwerken } \\ & =-ax+\frac{9}{2}a+\frac{13}{5}x-\frac{117}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{6}{15}+a)(\frac{14}{11}-q)& =(\color{red}{a}+\color{orange}{\frac{2}{5}}).(\color{green}{-q}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{14}{11}a-\frac{2}{5}q+\frac{2}{5}.\frac{14}{11}& \text{Uitwerken } \\ & =-aq+\frac{14}{11}a-\frac{2}{5}q+\frac{28}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-17}{9})(a-\frac{-2}{11})& =(\color{red}{p}+\color{orange}{\frac{17}{9}}).(\color{green}{a}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{17}{9})} . \color{green}{(a)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{11}p+\frac{17}{9}a+\frac{17}{9}.\frac{2}{11}& \text{Uitwerken } \\ & =ap+\frac{2}{11}p+\frac{17}{9}a+\frac{34}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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