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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-17}{6})(\frac{1}{15}-a)& =(\color{red}{a}+\color{orange}{\frac{-17}{6}}).(\color{green}{-a}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{15}a+\frac{17}{6}a-\frac{17}{6}.\frac{1}{15}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{15}+\frac{17}{6})a-\frac{17}{90} & \text{Neem samen} \\ &=-a^2+\frac{87}{30}a-\frac{17}{90} & \text{Maak de som} \\ &=-a^2+\frac{29}{10}a-\frac{17}{90} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{20}-a)(\frac{-19}{3}+q)& =(\color{red}{-a}+\color{orange}{\frac{-3}{5}}).(\color{green}{q}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{19}{3}a-\frac{3}{5}q+\frac{3}{5}.\frac{19}{3}& \text{Uitwerken } \\ & =-aq+\frac{19}{3}a-\frac{3}{5}q+\frac{57}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{19}{3}a-\frac{3}{5}q+\frac{19}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-1}{8}-x)(q-\frac{1}{11})& =(\color{red}{-x}+\color{orange}{\frac{-1}{8}}).(\color{green}{q}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{11}x-\frac{1}{8}q+\frac{1}{8}.\frac{1}{11}& \text{Uitwerken } \\ & =-qx+\frac{1}{11}x-\frac{1}{8}q+\frac{1}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-2}{5})(x+\frac{17}{13})& =(\color{red}{q}+\color{orange}{\frac{-2}{5}}).(\color{green}{x}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{13}q-\frac{2}{5}x-\frac{2}{5}.\frac{17}{13}& \text{Uitwerken } \\ & =qx+\frac{17}{13}q-\frac{2}{5}x-\frac{34}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p+\frac{10}{3})(p-\frac{-2}{4})& =(\color{red}{p}+\color{orange}{\frac{10}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{2}p+\frac{10}{3}p+\frac{10}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =p^2+(\frac{1}{2}+\frac{10}{3})p+\frac{10}{6} & \text{Neem samen} \\ &=p^2+\frac{23}{6}p+\frac{10}{6} & \text{Maak de som} \\ &=p^2+\frac{23}{6}p+\frac{5}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-1}{9})(p-\frac{20}{3})& =(\color{red}{q}+\color{orange}{\frac{-1}{9}}).(\color{green}{p}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{20}{3}q-\frac{1}{9}p+\frac{1}{9}.\frac{20}{3}& \text{Uitwerken } \\ & =pq-\frac{20}{3}q-\frac{1}{9}p+\frac{20}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+(-2))(\frac{-16}{16}-a)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(-2)} . \color{green}{(-a)} + \color{orange}{(-2)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ab-1b+2a+2.1& \text{Uitwerken } \\ & =-ab-1b+2a+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-9}{13}+x)(q-\frac{17}{20})& =(\color{red}{x}+\color{orange}{\frac{-9}{13}}).(\color{green}{q}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{20}x-\frac{9}{13}q+\frac{9}{13}.\frac{17}{20}& \text{Uitwerken } \\ & =qx-\frac{17}{20}x-\frac{9}{13}q+\frac{153}{260} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-14}{8})(a+\frac{1}{4})& =(\color{red}{p}+\color{orange}{\frac{-7}{4}}).(\color{green}{a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{4}p-\frac{7}{4}a-\frac{7}{4}.\frac{1}{4}& \text{Uitwerken } \\ & =ap+\frac{1}{4}p-\frac{7}{4}a-\frac{7}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{12}{8})(p-\frac{1}{18})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{18}a+\frac{3}{2}p-\frac{3}{2}.\frac{1}{18}& \text{Uitwerken } \\ & =ap-\frac{1}{18}a+\frac{3}{2}p-\frac{3}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{1}{18}a+\frac{3}{2}p-\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{18}-p)(\frac{-3}{10}-b)& =(\color{red}{-p}+\color{orange}{\frac{2}{9}}).(\color{green}{-b}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{2}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{10}p-\frac{2}{9}b-\frac{2}{9}.\frac{3}{10}& \text{Uitwerken } \\ & =bp+\frac{3}{10}p-\frac{2}{9}b-\frac{6}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{3}{10}p-\frac{2}{9}b-\frac{1}{15} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-16}{8}-b)(p+\frac{-1}{12})& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{12}b-2p+2.\frac{1}{12}& \text{Uitwerken } \\ & =-bp+\frac{1}{12}b-2p+\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{1}{12}b-2p+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
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