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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{10}{5}-x)(x-\frac{5}{6})& =(\color{red}{-x}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{5}{6}x+2x-2.\frac{5}{6}& \text{Uitwerken } \\ & =-x^2+(\frac{5}{6}+2)x-\frac{10}{6} & \text{Neem samen} \\ &=-x^2+\frac{17}{6}x-\frac{10}{6} & \text{Maak de som} \\ &=-x^2+\frac{17}{6}x-\frac{5}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{11}-q)(\frac{14}{14}+q)& =(\color{red}{-q}+\color{orange}{\frac{19}{11}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{19}{11})} . \color{green}{(q)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -qq-1q+\frac{19}{11}q+\frac{19}{11}.1& \text{Uitwerken } \\ & =-q^2+((-1)+\frac{19}{11})q+(\frac{-19}{11}) & \text{Neem samen} \\ &=-q^2+\frac{8}{11}q+(\frac{-19}{11}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-16}{13})(q+\frac{-3}{19})& =(\color{red}{a}+\color{orange}{\frac{16}{13}}).(\color{green}{q}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{16}{13})} . \color{green}{(q)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{19}a+\frac{16}{13}q-\frac{16}{13}.\frac{3}{19}& \text{Uitwerken } \\ & =aq-\frac{3}{19}a+\frac{16}{13}q-\frac{48}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-6}{7}-x)(q-\frac{-9}{3})& =(\color{red}{-x}+\color{orange}{\frac{-6}{7}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(3)} + \color{orange}{(\frac{-6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -qx-3x-\frac{6}{7}q-\frac{6}{7}.3& \text{Uitwerken } \\ & =-qx-3x-\frac{6}{7}q-\frac{18}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{6}{16})(\frac{-17}{7}+q)& =(\color{red}{b}+\color{orange}{\frac{3}{8}}).(\color{green}{q}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{7}b+\frac{3}{8}q-\frac{3}{8}.\frac{17}{7}& \text{Uitwerken } \\ & =bq-\frac{17}{7}b+\frac{3}{8}q-\frac{51}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{14}-b)(\frac{-5}{4}+p)& =(\color{red}{-b}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{4}b-\frac{1}{2}p+\frac{1}{2}.\frac{5}{4}& \text{Uitwerken } \\ & =-bp+\frac{5}{4}b-\frac{1}{2}p+\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{16}{3}-q)(p-\frac{-20}{8})& =(\color{red}{-q}+\color{orange}{\frac{16}{3}}).(\color{green}{p}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{16}{3})} . \color{green}{(p)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{2}q+\frac{16}{3}p+\frac{16}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =-pq-\frac{5}{2}q+\frac{16}{3}p+\frac{80}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{5}{2}q+\frac{16}{3}p+\frac{40}{3} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{7}{7}+x)(p-\frac{-6}{10})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{5}x+1p+1.\frac{3}{5}& \text{Uitwerken } \\ & =px+\frac{3}{5}x+1p+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{20}{10})(\frac{5}{6}-q)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{-q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(2)} . \color{green}{(-q)} + \color{orange}{(2)} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{5}{6}q-2q+2.\frac{5}{6}& \text{Uitwerken } \\ & =-q^2+(\frac{5}{6}+(-2))q+(\frac{-10}{6}) & \text{Neem samen} \\ &=-q^2-\frac{7}{6}q+(\frac{-10}{6}) & \text{Maak de som} \\ &=-q^2-\frac{7}{6}q+(\frac{-5}{3}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(p+\frac{10}{15})(\frac{17}{4}+p)& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{17}{4}p+\frac{2}{3}p+\frac{2}{3}.\frac{17}{4}& \text{Uitwerken } \\ & =p^2+(\frac{17}{4}+\frac{2}{3})p+\frac{34}{12} & \text{Neem samen} \\ &=p^2+\frac{59}{12}p+\frac{34}{12} & \text{Maak de som} \\ &=p^2+\frac{59}{12}p+\frac{17}{6} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{15}{2}+x)(q+\frac{13}{10})& =(\color{red}{x}+\color{orange}{\frac{15}{2}}).(\color{green}{q}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{15}{2})} . \color{green}{(q)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{10}x+\frac{15}{2}q+\frac{15}{2}.\frac{13}{10}& \text{Uitwerken } \\ & =qx+\frac{13}{10}x+\frac{15}{2}q+\frac{195}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{13}{10}x+\frac{15}{2}q+\frac{39}{4} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-13}{18})(18+x)& =(\color{red}{q}+\color{orange}{\frac{-13}{18}}).(\color{green}{x}+\color{blue}{18})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(18)} + \color{orange}{(\frac{-13}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = qx+18q-\frac{13}{18}x-\frac{13}{18}.18& \text{Uitwerken } \\ & =qx+18q-\frac{13}{18}x-\frac{234}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+18q-\frac{13}{18}x-13 & \text{Vereenvoudig} \\\end{align}\)
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