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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{12}+p)(\frac{5}{13}-a)& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{-a}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{13}p-\frac{3}{4}a+\frac{3}{4}.\frac{5}{13}& \text{Uitwerken } \\ & =-ap+\frac{5}{13}p-\frac{3}{4}a+\frac{15}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-6}{16}+p)(q-\frac{12}{13})& =(\color{red}{p}+\color{orange}{\frac{-3}{8}}).(\color{green}{q}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{12}{13}p-\frac{3}{8}q+\frac{3}{8}.\frac{12}{13}& \text{Uitwerken } \\ & =pq-\frac{12}{13}p-\frac{3}{8}q+\frac{36}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{12}{13}p-\frac{3}{8}q+\frac{9}{26} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p-\frac{9}{16})(a+\frac{-16}{6})& =(\color{red}{p}+\color{orange}{\frac{-9}{16}}).(\color{green}{a}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{8}{3}p-\frac{9}{16}a+\frac{9}{16}.\frac{8}{3}& \text{Uitwerken } \\ & =ap-\frac{8}{3}p-\frac{9}{16}a+\frac{72}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{8}{3}p-\frac{9}{16}a+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-10}{12}+p)(\frac{9}{7}-b)& =(\color{red}{p}+\color{orange}{\frac{-5}{6}}).(\color{green}{-b}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{7}p+\frac{5}{6}b-\frac{5}{6}.\frac{9}{7}& \text{Uitwerken } \\ & =-bp+\frac{9}{7}p+\frac{5}{6}b-\frac{45}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{9}{7}p+\frac{5}{6}b-\frac{15}{14} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{5}+a)(q-\frac{12}{5})& =(\color{red}{a}+\color{orange}{\frac{16}{5}}).(\color{green}{q}+\color{blue}{\frac{-12}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{5})} + \color{orange}{(\frac{16}{5})} . \color{green}{(q)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(\frac{-12}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{12}{5}a+\frac{16}{5}q-\frac{16}{5}.\frac{12}{5}& \text{Uitwerken } \\ & =aq-\frac{12}{5}a+\frac{16}{5}q-\frac{192}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-5}{19})(x-\frac{-9}{13})& =(\color{red}{p}+\color{orange}{\frac{-5}{19}}).(\color{green}{x}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{13}p-\frac{5}{19}x-\frac{5}{19}.\frac{9}{13}& \text{Uitwerken } \\ & =px+\frac{9}{13}p-\frac{5}{19}x-\frac{45}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-15}{8})(3+q)& =(\color{red}{a}+\color{orange}{\frac{15}{8}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{15}{8})} . \color{green}{(q)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = aq+3a+\frac{15}{8}q+\frac{15}{8}.3& \text{Uitwerken } \\ & =aq+3a+\frac{15}{8}q+\frac{45}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{17}{9})(\frac{6}{13}+p)& =(\color{red}{q}+\color{orange}{\frac{-17}{9}}).(\color{green}{p}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{6}{13}q-\frac{17}{9}p-\frac{17}{9}.\frac{6}{13}& \text{Uitwerken } \\ & =pq+\frac{6}{13}q-\frac{17}{9}p-\frac{102}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{6}{13}q-\frac{17}{9}p-\frac{34}{39} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p+\frac{2}{14})(a+\frac{16}{19})& =(\color{red}{p}+\color{orange}{\frac{1}{7}}).(\color{green}{a}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{1}{7})} . \color{green}{(a)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{19}p+\frac{1}{7}a+\frac{1}{7}.\frac{16}{19}& \text{Uitwerken } \\ & =ap+\frac{16}{19}p+\frac{1}{7}a+\frac{16}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{16}{6})(\frac{14}{13}+q)& =(\color{red}{a}+\color{orange}{\frac{8}{3}}).(\color{green}{q}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(\frac{8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{14}{13}a+\frac{8}{3}q+\frac{8}{3}.\frac{14}{13}& \text{Uitwerken } \\ & =aq+\frac{14}{13}a+\frac{8}{3}q+\frac{112}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{13}{9}+x)(\frac{-14}{14}+b)& =(\color{red}{x}+\color{orange}{\frac{13}{9}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{13}{9})} . \color{green}{(b)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx-1x+\frac{13}{9}b-\frac{13}{9}.1& \text{Uitwerken } \\ & =bx-1x+\frac{13}{9}b-\frac{13}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-17}{5}-a)(x+\frac{5}{16})& =(\color{red}{-a}+\color{orange}{\frac{-17}{5}}).(\color{green}{x}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{5}{16}a-\frac{17}{5}x-\frac{17}{5}.\frac{5}{16}& \text{Uitwerken } \\ & =-ax-\frac{5}{16}a-\frac{17}{5}x-\frac{85}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{5}{16}a-\frac{17}{5}x-\frac{17}{16} & \text{Vereenvoudig} \\\end{align}\)
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