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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{13}{7}-p)(q+\frac{-13}{11})& =(\color{red}{-p}+\color{orange}{\frac{13}{7}}).(\color{green}{q}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{13}{7})} . \color{green}{(q)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{13}{11}p+\frac{13}{7}q-\frac{13}{7}.\frac{13}{11}& \text{Uitwerken } \\ & =-pq+\frac{13}{11}p+\frac{13}{7}q-\frac{169}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-14}{3}+p)(\frac{-16}{6}-x)& =(\color{red}{p}+\color{orange}{\frac{-14}{3}}).(\color{green}{-x}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{8}{3}p+\frac{14}{3}x+\frac{14}{3}.\frac{8}{3}& \text{Uitwerken } \\ & =-px-\frac{8}{3}p+\frac{14}{3}x+\frac{112}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-14}{11})(\frac{-12}{16}+b)& =(\color{red}{x}+\color{orange}{\frac{14}{11}}).(\color{green}{b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{14}{11})} . \color{green}{(b)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{4}x+\frac{14}{11}b-\frac{14}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =bx-\frac{3}{4}x+\frac{14}{11}b-\frac{42}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{3}{4}x+\frac{14}{11}b-\frac{21}{22} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b-\frac{-7}{7})(x-\frac{2}{17})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{17}b+1x-1.\frac{2}{17}& \text{Uitwerken } \\ & =bx-\frac{2}{17}b+1x-\frac{2}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-6}{19})(\frac{19}{4}+x)& =(\color{red}{q}+\color{orange}{\frac{6}{19}}).(\color{green}{x}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{6}{19})} . \color{green}{(x)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{4}q+\frac{6}{19}x+\frac{6}{19}.\frac{19}{4}& \text{Uitwerken } \\ & =qx+\frac{19}{4}q+\frac{6}{19}x+\frac{114}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{19}{4}q+\frac{6}{19}x+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-12}{4})(\frac{-1}{18}+b)& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{18}x-3b+3.\frac{1}{18}& \text{Uitwerken } \\ & =bx-\frac{1}{18}x-3b+\frac{3}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{18}x-3b+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+\frac{12}{20})(x-\frac{-10}{10})& =(\color{red}{p}+\color{orange}{\frac{3}{5}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1p+\frac{3}{5}x+\frac{3}{5}.1& \text{Uitwerken } \\ & =px+1p+\frac{3}{5}x+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{20}{18})(p-\frac{-1}{20})& =(\color{red}{x}+\color{orange}{\frac{10}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{10}{9})} . \color{green}{(p)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{20}x+\frac{10}{9}p+\frac{10}{9}.\frac{1}{20}& \text{Uitwerken } \\ & =px+\frac{1}{20}x+\frac{10}{9}p+\frac{10}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{20}x+\frac{10}{9}p+\frac{1}{18} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{13}{11}-p)(\frac{15}{12}+b)& =(\color{red}{-p}+\color{orange}{\frac{13}{11}}).(\color{green}{b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{13}{11})} . \color{green}{(b)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{5}{4}p+\frac{13}{11}b+\frac{13}{11}.\frac{5}{4}& \text{Uitwerken } \\ & =-bp-\frac{5}{4}p+\frac{13}{11}b+\frac{65}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-3}{16}-q)(b-\frac{-10}{12})& =(\color{red}{-q}+\color{orange}{\frac{-3}{16}}).(\color{green}{b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{6}q-\frac{3}{16}b-\frac{3}{16}.\frac{5}{6}& \text{Uitwerken } \\ & =-bq-\frac{5}{6}q-\frac{3}{16}b-\frac{15}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{5}{6}q-\frac{3}{16}b-\frac{5}{32} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-1}{7}+q)(\frac{-20}{4}-x)& =(\color{red}{q}+\color{orange}{\frac{-1}{7}}).(\color{green}{-x}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(-5)} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -qx-5q+\frac{1}{7}x+\frac{1}{7}.5& \text{Uitwerken } \\ & =-qx-5q+\frac{1}{7}x+\frac{5}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{9}+p)(a-\frac{-19}{6})& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{a}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{6}p-\frac{5}{3}a-\frac{5}{3}.\frac{19}{6}& \text{Uitwerken } \\ & =ap+\frac{19}{6}p-\frac{5}{3}a-\frac{95}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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