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

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

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Verbetersleutel

  1. \(\begin{align}(b+\frac{-13}{2})(\frac{14}{11}+b)& =(\color{red}{b}+\color{orange}{\frac{-13}{2}}).(\color{green}{b}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{14}{11}b-\frac{13}{2}b-\frac{13}{2}.\frac{14}{11}& \text{Uitwerken } \\ & =b^2+(\frac{14}{11}+(\frac{-13}{2}))b-(\frac{-182}{22}) & \text{Neem samen} \\ &=b^2-\frac{115}{22}b-(\frac{-182}{22}) & \text{Maak de som} \\ &=b^2-\frac{115}{22}b+\frac{91}{11} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(\frac{-5}{8}-q)(\frac{-10}{13}-b)& =(\color{red}{-q}+\color{orange}{\frac{-5}{8}}).(\color{green}{-b}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{10}{13}q+\frac{5}{8}b+\frac{5}{8}.\frac{10}{13}& \text{Uitwerken } \\ & =bq+\frac{10}{13}q+\frac{5}{8}b+\frac{50}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{10}{13}q+\frac{5}{8}b+\frac{25}{52} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{14}-a)(p-\frac{-2}{10})& =(\color{red}{-a}+\color{orange}{\frac{3}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{5}a+\frac{3}{7}p+\frac{3}{7}.\frac{1}{5}& \text{Uitwerken } \\ & =-ap-\frac{1}{5}a+\frac{3}{7}p+\frac{3}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{14}-x)(x-\frac{-13}{14})& =(\color{red}{-x}+\color{orange}{\frac{9}{14}}).(\color{green}{x}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{9}{14})} . \color{green}{(x)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{13}{14}x+\frac{9}{14}x+\frac{9}{14}.\frac{13}{14}& \text{Uitwerken } \\ & =-x^2+((\frac{-13}{14})+\frac{9}{14})x+(\frac{-117}{196}) & \text{Neem samen} \\ &=-x^2-\frac{4}{14}x+(\frac{-117}{196}) & \text{Maak de som} \\ &=-x^2-\frac{2}{7}x+(\frac{-117}{196}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(p-\frac{15}{12})(x+\frac{-20}{6})& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{x}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{3}p-\frac{5}{4}x+\frac{5}{4}.\frac{10}{3}& \text{Uitwerken } \\ & =px-\frac{10}{3}p-\frac{5}{4}x+\frac{50}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{10}{3}p-\frac{5}{4}x+\frac{25}{6} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{6}{5})(x-\frac{3}{14})& =(\color{red}{b}+\color{orange}{\frac{6}{5}}).(\color{green}{x}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{14}b+\frac{6}{5}x-\frac{6}{5}.\frac{3}{14}& \text{Uitwerken } \\ & =bx-\frac{3}{14}b+\frac{6}{5}x-\frac{18}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{3}{14}b+\frac{6}{5}x-\frac{9}{35} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{9}-q)(b+\frac{1}{12})& =(\color{red}{-q}+\color{orange}{\frac{-14}{9}}).(\color{green}{b}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{12}q-\frac{14}{9}b-\frac{14}{9}.\frac{1}{12}& \text{Uitwerken } \\ & =-bq-\frac{1}{12}q-\frac{14}{9}b-\frac{14}{108} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{12}q-\frac{14}{9}b-\frac{7}{54} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-1}{6})(\frac{-6}{18}+q)& =(\color{red}{a}+\color{orange}{\frac{1}{6}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{3}a+\frac{1}{6}q-\frac{1}{6}.\frac{1}{3}& \text{Uitwerken } \\ & =aq-\frac{1}{3}a+\frac{1}{6}q-\frac{1}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-15}{8}-a)(p-(-11))& =(\color{red}{-a}+\color{orange}{\frac{-15}{8}}).(\color{green}{p}+\color{blue}{11})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(11)} + \color{orange}{(\frac{-15}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = -ap-11a-\frac{15}{8}p-\frac{15}{8}.11& \text{Uitwerken } \\ & =-ap-11a-\frac{15}{8}p-\frac{165}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-11}{6}+b)(p-\frac{16}{11})& =(\color{red}{b}+\color{orange}{\frac{-11}{6}}).(\color{green}{p}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{16}{11}b-\frac{11}{6}p+\frac{11}{6}.\frac{16}{11}& \text{Uitwerken } \\ & =bp-\frac{16}{11}b-\frac{11}{6}p+\frac{176}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{16}{11}b-\frac{11}{6}p+\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{3}+a)(\frac{15}{2}+q)& =(\color{red}{a}+\color{orange}{\frac{-19}{3}}).(\color{green}{q}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{15}{2}a-\frac{19}{3}q-\frac{19}{3}.\frac{15}{2}& \text{Uitwerken } \\ & =aq+\frac{15}{2}a-\frac{19}{3}q-\frac{285}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{15}{2}a-\frac{19}{3}q-\frac{95}{2} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q-\frac{16}{2})(\frac{14}{7}-q)& =(\color{red}{q}+\color{orange}{(-8)}).(\color{green}{-q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(-8)} . \color{green}{(-q)} + \color{orange}{(-8)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qq+2q+8q-8.2& \text{Uitwerken } \\ & =-q^2+(2+8)q-16 & \text{Neem samen} \\ &=-q^2+10q-16 & \text{Maak de som} \\\end{align}\)
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