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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-20}{8}+q)(b-\frac{5}{2})& =(\color{red}{q}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{2}q-\frac{5}{2}b+\frac{5}{2}.\frac{5}{2}& \text{Uitwerken } \\ & =bq-\frac{5}{2}q-\frac{5}{2}b+\frac{25}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{10}{12}+b)(p+\frac{10}{2})& =(\color{red}{b}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(5)} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bp+5b+\frac{5}{6}p+\frac{5}{6}.5& \text{Uitwerken } \\ & =bp+5b+\frac{5}{6}p+\frac{25}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{12}{19}+q)(\frac{-8}{17}-p)& =(\color{red}{q}+\color{orange}{\frac{12}{19}}).(\color{green}{-p}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{12}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{8}{17}q-\frac{12}{19}p-\frac{12}{19}.\frac{8}{17}& \text{Uitwerken } \\ & =-pq-\frac{8}{17}q-\frac{12}{19}p-\frac{96}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{11}-p)((-6)-a)& =(\color{red}{-p}+\color{orange}{\frac{9}{11}}).(\color{green}{-a}+\color{blue}{(-6)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(-6)} + \color{orange}{(\frac{9}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ap+6p-\frac{9}{11}a-\frac{9}{11}.6& \text{Uitwerken } \\ & =ap+6p-\frac{9}{11}a-\frac{54}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{3}{11})(x+\frac{-14}{17})& =(\color{red}{p}+\color{orange}{\frac{-3}{11}}).(\color{green}{x}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{14}{17}p-\frac{3}{11}x+\frac{3}{11}.\frac{14}{17}& \text{Uitwerken } \\ & =px-\frac{14}{17}p-\frac{3}{11}x+\frac{42}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-5}{9})(x+\frac{1}{4})& =(\color{red}{q}+\color{orange}{\frac{-5}{9}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{4}q-\frac{5}{9}x-\frac{5}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =qx+\frac{1}{4}q-\frac{5}{9}x-\frac{5}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-13}{15})(\frac{18}{5}+q)& =(\color{red}{p}+\color{orange}{\frac{13}{15}}).(\color{green}{q}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{13}{15})} . \color{green}{(q)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{18}{5}p+\frac{13}{15}q+\frac{13}{15}.\frac{18}{5}& \text{Uitwerken } \\ & =pq+\frac{18}{5}p+\frac{13}{15}q+\frac{234}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{18}{5}p+\frac{13}{15}q+\frac{78}{25} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{3}{11}-q)(b+\frac{13}{12})& =(\color{red}{-q}+\color{orange}{\frac{3}{11}}).(\color{green}{b}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{3}{11})} . \color{green}{(b)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{12}q+\frac{3}{11}b+\frac{3}{11}.\frac{13}{12}& \text{Uitwerken } \\ & =-bq-\frac{13}{12}q+\frac{3}{11}b+\frac{39}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{13}{12}q+\frac{3}{11}b+\frac{13}{44} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{9}{8})(\frac{7}{17}+x)& =(\color{red}{b}+\color{orange}{\frac{-9}{8}}).(\color{green}{x}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{17}b-\frac{9}{8}x-\frac{9}{8}.\frac{7}{17}& \text{Uitwerken } \\ & =bx+\frac{7}{17}b-\frac{9}{8}x-\frac{63}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{13}{17})(b+\frac{-3}{19})& =(\color{red}{q}+\color{orange}{\frac{-13}{17}}).(\color{green}{b}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{19}q-\frac{13}{17}b+\frac{13}{17}.\frac{3}{19}& \text{Uitwerken } \\ & =bq-\frac{3}{19}q-\frac{13}{17}b+\frac{39}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{12}{11})(x-(-6))& =(\color{red}{a}+\color{orange}{\frac{12}{11}}).(\color{green}{x}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(6)} + \color{orange}{(\frac{12}{11})} . \color{green}{(x)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = ax+6a+\frac{12}{11}x+\frac{12}{11}.6& \text{Uitwerken } \\ & =ax+6a+\frac{12}{11}x+\frac{72}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{12}{19})(b-\frac{16}{19})& =(\color{red}{x}+\color{orange}{\frac{12}{19}}).(\color{green}{b}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{12}{19})} . \color{green}{(b)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{16}{19}x+\frac{12}{19}b-\frac{12}{19}.\frac{16}{19}& \text{Uitwerken } \\ & =bx-\frac{16}{19}x+\frac{12}{19}b-\frac{192}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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