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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{14}{6})(\frac{2}{8}-q)& =(\color{red}{b}+\color{orange}{\frac{7}{3}}).(\color{green}{-q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{7}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{4}b-\frac{7}{3}q+\frac{7}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =-bq+\frac{1}{4}b-\frac{7}{3}q+\frac{7}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-18}{11}-p)(p-\frac{20}{2})& =(\color{red}{-p}+\color{orange}{\frac{-18}{11}}).(\color{green}{p}+\color{blue}{(-10)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(-10)} + \color{orange}{(\frac{-18}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{11})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -pp+10p-\frac{18}{11}p+\frac{18}{11}.10& \text{Uitwerken } \\ & =-p^2+(10+(\frac{-18}{11}))p+(\frac{-180}{11}) & \text{Neem samen} \\ &=-p^2+\frac{92}{11}p+(\frac{-180}{11}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(p-\frac{17}{10})(q-\frac{-14}{3})& =(\color{red}{p}+\color{orange}{\frac{-17}{10}}).(\color{green}{q}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{14}{3}p-\frac{17}{10}q-\frac{17}{10}.\frac{14}{3}& \text{Uitwerken } \\ & =pq+\frac{14}{3}p-\frac{17}{10}q-\frac{238}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{14}{3}p-\frac{17}{10}q-\frac{119}{15} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-3}{4}-b)(\frac{7}{13}-p)& =(\color{red}{-b}+\color{orange}{\frac{-3}{4}}).(\color{green}{-p}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{13}b+\frac{3}{4}p-\frac{3}{4}.\frac{7}{13}& \text{Uitwerken } \\ & =bp-\frac{7}{13}b+\frac{3}{4}p-\frac{21}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{16}-x)(\frac{5}{3}-q)& =(\color{red}{-x}+\color{orange}{\frac{5}{16}}).(\color{green}{-q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{5}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{3}x-\frac{5}{16}q+\frac{5}{16}.\frac{5}{3}& \text{Uitwerken } \\ & =qx-\frac{5}{3}x-\frac{5}{16}q+\frac{25}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{15}-q)(\frac{-20}{20}+q)& =(\color{red}{-q}+\color{orange}{\frac{-7}{15}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-7}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qq+1q-\frac{7}{15}q+\frac{7}{15}.1& \text{Uitwerken } \\ & =-q^2+(1+(\frac{-7}{15}))q+(\frac{-7}{15}) & \text{Neem samen} \\ &=-q^2+\frac{8}{15}q+(\frac{-7}{15}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-15}{20}-x)(q+\frac{4}{13})& =(\color{red}{-x}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{4}{13}x-\frac{3}{4}q-\frac{3}{4}.\frac{4}{13}& \text{Uitwerken } \\ & =-qx-\frac{4}{13}x-\frac{3}{4}q-\frac{12}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{4}{13}x-\frac{3}{4}q-\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{20}+a)(\frac{8}{18}-b)& =(\color{red}{a}+\color{orange}{\frac{1}{5}}).(\color{green}{-b}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{4}{9}a-\frac{1}{5}b+\frac{1}{5}.\frac{4}{9}& \text{Uitwerken } \\ & =-ab+\frac{4}{9}a-\frac{1}{5}b+\frac{4}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+\frac{18}{12})(\frac{18}{6}-a)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{-a}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{3}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -ax+3x-\frac{3}{2}a+\frac{3}{2}.3& \text{Uitwerken } \\ & =-ax+3x-\frac{3}{2}a+\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{5}+q)(p+\frac{-12}{10})& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{p}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{6}{5}q+\frac{3}{5}p-\frac{3}{5}.\frac{6}{5}& \text{Uitwerken } \\ & =pq-\frac{6}{5}q+\frac{3}{5}p-\frac{18}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{15}-p)(\frac{-17}{16}+b)& =(\color{red}{-p}+\color{orange}{\frac{-14}{15}}).(\color{green}{b}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{-14}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{17}{16}p-\frac{14}{15}b+\frac{14}{15}.\frac{17}{16}& \text{Uitwerken } \\ & =-bp+\frac{17}{16}p-\frac{14}{15}b+\frac{238}{240} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{17}{16}p-\frac{14}{15}b+\frac{119}{120} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{14}{13}+x)(\frac{-20}{17}-a)& =(\color{red}{x}+\color{orange}{\frac{14}{13}}).(\color{green}{-a}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{14}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{20}{17}x-\frac{14}{13}a-\frac{14}{13}.\frac{20}{17}& \text{Uitwerken } \\ & =-ax-\frac{20}{17}x-\frac{14}{13}a-\frac{280}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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