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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-2}{11})(\frac{19}{20}-x)& =(\color{red}{a}+\color{orange}{\frac{-2}{11}}).(\color{green}{-x}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{19}{20}a+\frac{2}{11}x-\frac{2}{11}.\frac{19}{20}& \text{Uitwerken } \\ & =-ax+\frac{19}{20}a+\frac{2}{11}x-\frac{38}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{19}{20}a+\frac{2}{11}x-\frac{19}{110} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-2}{6}+q)(\frac{17}{10}-a)& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{-a}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{17}{10}q+\frac{1}{3}a-\frac{1}{3}.\frac{17}{10}& \text{Uitwerken } \\ & =-aq+\frac{17}{10}q+\frac{1}{3}a-\frac{17}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-15}{14})(x+\frac{12}{5})& =(\color{red}{q}+\color{orange}{\frac{-15}{14}}).(\color{green}{x}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{5}q-\frac{15}{14}x-\frac{15}{14}.\frac{12}{5}& \text{Uitwerken } \\ & =qx+\frac{12}{5}q-\frac{15}{14}x-\frac{180}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{5}q-\frac{15}{14}x-\frac{18}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{3}{7})(a-\frac{-8}{19})& =(\color{red}{a}+\color{orange}{\frac{-3}{7}}).(\color{green}{a}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{8}{19}a-\frac{3}{7}a-\frac{3}{7}.\frac{8}{19}& \text{Uitwerken } \\ & =a^2+(\frac{8}{19}+(\frac{-3}{7}))a-(\frac{-24}{133}) & \text{Neem samen} \\ &=a^2-\frac{1}{133}a-(\frac{-24}{133}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{6}+p)(\frac{-18}{13}-x)& =(\color{red}{p}+\color{orange}{\frac{-8}{3}}).(\color{green}{-x}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{18}{13}p+\frac{8}{3}x+\frac{8}{3}.\frac{18}{13}& \text{Uitwerken } \\ & =-px-\frac{18}{13}p+\frac{8}{3}x+\frac{144}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{18}{13}p+\frac{8}{3}x+\frac{48}{13} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-6}{18})(q-\frac{-7}{8})& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{8}x-\frac{1}{3}q-\frac{1}{3}.\frac{7}{8}& \text{Uitwerken } \\ & =qx+\frac{7}{8}x-\frac{1}{3}q-\frac{7}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-12}{2})(p+\frac{12}{18})& =(\color{red}{p}+\color{orange}{6}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(6)} . \color{green}{(p)} + \color{orange}{(6)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{2}{3}p+6p+6.\frac{2}{3}& \text{Uitwerken } \\ & =p^2+(\frac{2}{3}+6)p+\frac{12}{3} & \text{Neem samen} \\ &=p^2+\frac{20}{3}p+\frac{12}{3} & \text{Maak de som} \\ &=p^2+\frac{20}{3}p+4 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-18}{12})(\frac{-16}{7}-x)& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{-x}+\color{blue}{\frac{-16}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{7})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-16}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{16}{7}b-\frac{3}{2}x-\frac{3}{2}.\frac{16}{7}& \text{Uitwerken } \\ & =-bx-\frac{16}{7}b-\frac{3}{2}x-\frac{48}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{16}{7}b-\frac{3}{2}x-\frac{24}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-7}{12})(x+\frac{-2}{8})& =(\color{red}{q}+\color{orange}{\frac{7}{12}}).(\color{green}{x}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{7}{12})} . \color{green}{(x)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{4}q+\frac{7}{12}x-\frac{7}{12}.\frac{1}{4}& \text{Uitwerken } \\ & =qx-\frac{1}{4}q+\frac{7}{12}x-\frac{7}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-15}{11}-q)(p-\frac{13}{2})& =(\color{red}{-q}+\color{orange}{\frac{-15}{11}}).(\color{green}{p}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{13}{2}q-\frac{15}{11}p+\frac{15}{11}.\frac{13}{2}& \text{Uitwerken } \\ & =-pq+\frac{13}{2}q-\frac{15}{11}p+\frac{195}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{9}{19})(\frac{8}{6}+a)& =(\color{red}{p}+\color{orange}{\frac{9}{19}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{9}{19})} . \color{green}{(a)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{3}p+\frac{9}{19}a+\frac{9}{19}.\frac{4}{3}& \text{Uitwerken } \\ & =ap+\frac{4}{3}p+\frac{9}{19}a+\frac{36}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{4}{3}p+\frac{9}{19}a+\frac{12}{19} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{3}-b)(p-\frac{-17}{9})& =(\color{red}{-b}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{17}{9}b-6p-6.\frac{17}{9}& \text{Uitwerken } \\ & =-bp-\frac{17}{9}b-6p-\frac{102}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{17}{9}b-6p-\frac{34}{3} & \text{Vereenvoudig} \\\end{align}\)
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