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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-16}{19}-a)(q-\frac{16}{4})& =(\color{red}{-a}+\color{orange}{\frac{-16}{19}}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-16}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -aq+4a-\frac{16}{19}q+\frac{16}{19}.4& \text{Uitwerken } \\ & =-aq+4a-\frac{16}{19}q+\frac{64}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-10}{12}+q)(\frac{-6}{8}-b)& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{-b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{4}q+\frac{5}{6}b+\frac{5}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =-bq-\frac{3}{4}q+\frac{5}{6}b+\frac{15}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{3}{4}q+\frac{5}{6}b+\frac{5}{8} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-15}{3})(\frac{-7}{15}-a)& =(\color{red}{p}+\color{orange}{5}).(\color{green}{-a}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(5)} . \color{green}{(-a)} + \color{orange}{(5)} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{7}{15}p-5a-5.\frac{7}{15}& \text{Uitwerken } \\ & =-ap-\frac{7}{15}p-5a-\frac{35}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{7}{15}p-5a-\frac{7}{3} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-8}{15})(\frac{-9}{6}+a)& =(\color{red}{a}+\color{orange}{\frac{8}{15}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{8}{15})} . \color{green}{(a)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{2}a+\frac{8}{15}a-\frac{8}{15}.\frac{3}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{2})+\frac{8}{15})a-(\frac{-24}{30}) & \text{Neem samen} \\ &=a^2-\frac{29}{30}a-(\frac{-24}{30}) & \text{Maak de som} \\ &=a^2-\frac{29}{30}a+\frac{4}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{18}{19}-a)(a+\frac{3}{2})& =(\color{red}{-a}+\color{orange}{\frac{18}{19}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{18}{19})} . \color{green}{(a)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{3}{2}a+\frac{18}{19}a+\frac{18}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-3}{2})+\frac{18}{19})a+(\frac{-54}{38}) & \text{Neem samen} \\ &=-a^2-\frac{21}{38}a+(\frac{-54}{38}) & \text{Maak de som} \\ &=-a^2-\frac{21}{38}a+(\frac{-27}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{-8}{17}-q)(a+\frac{-9}{16})& =(\color{red}{-q}+\color{orange}{\frac{-8}{17}}).(\color{green}{a}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{16}q-\frac{8}{17}a+\frac{8}{17}.\frac{9}{16}& \text{Uitwerken } \\ & =-aq+\frac{9}{16}q-\frac{8}{17}a+\frac{72}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{9}{16}q-\frac{8}{17}a+\frac{9}{34} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-2}{11})(\frac{20}{4}+p)& =(\color{red}{q}+\color{orange}{\frac{-2}{11}}).(\color{green}{p}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(\frac{-2}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = pq+5q-\frac{2}{11}p-\frac{2}{11}.5& \text{Uitwerken } \\ & =pq+5q-\frac{2}{11}p-\frac{10}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{9}{16}+a)(x-\frac{-12}{11})& =(\color{red}{a}+\color{orange}{\frac{9}{16}}).(\color{green}{x}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{9}{16})} . \color{green}{(x)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{12}{11}a+\frac{9}{16}x+\frac{9}{16}.\frac{12}{11}& \text{Uitwerken } \\ & =ax+\frac{12}{11}a+\frac{9}{16}x+\frac{108}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{12}{11}a+\frac{9}{16}x+\frac{27}{44} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{2}{11})(\frac{15}{20}+q)& =(\color{red}{b}+\color{orange}{\frac{-2}{11}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{4}b-\frac{2}{11}q-\frac{2}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =bq+\frac{3}{4}b-\frac{2}{11}q-\frac{6}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{3}{4}b-\frac{2}{11}q-\frac{3}{22} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-6}{12})(\frac{-1}{7}-q)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{-q}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{7}b-\frac{1}{2}q-\frac{1}{2}.\frac{1}{7}& \text{Uitwerken } \\ & =-bq-\frac{1}{7}b-\frac{1}{2}q-\frac{1}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{7}{15})(x+\frac{-2}{3})& =(\color{red}{a}+\color{orange}{\frac{-7}{15}}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{3}a-\frac{7}{15}x+\frac{7}{15}.\frac{2}{3}& \text{Uitwerken } \\ & =ax-\frac{2}{3}a-\frac{7}{15}x+\frac{14}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-3}{16}-a)(\frac{12}{20}+p)& =(\color{red}{-a}+\color{orange}{\frac{-3}{16}}).(\color{green}{p}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{5}a-\frac{3}{16}p-\frac{3}{16}.\frac{3}{5}& \text{Uitwerken } \\ & =-ap-\frac{3}{5}a-\frac{3}{16}p-\frac{9}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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