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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{5}{14})(q-14)& =(\color{red}{p}+\color{orange}{\frac{-5}{14}}).(\color{green}{q}+\color{blue}{(-14)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-14)} + \color{orange}{(\frac{-5}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = pq-14p-\frac{5}{14}q+\frac{5}{14}.14& \text{Uitwerken } \\ & =pq-14p-\frac{5}{14}q+\frac{70}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-14p-\frac{5}{14}q+5 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{2}{11}-a)(\frac{-16}{2}+x)& =(\color{red}{-a}+\color{orange}{\frac{2}{11}}).(\color{green}{x}+\color{blue}{(-8)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(-8)} + \color{orange}{(\frac{2}{11})} . \color{green}{(x)} + \color{orange}{(\frac{2}{11})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = -ax+8a+\frac{2}{11}x-\frac{2}{11}.8& \text{Uitwerken } \\ & =-ax+8a+\frac{2}{11}x-\frac{16}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{5}{3}+x)(\frac{-10}{4}-x)& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{-x}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{5}{2}x-\frac{5}{3}x-\frac{5}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =-x^2+((\frac{-5}{2})+(\frac{-5}{3}))x-\frac{25}{6} & \text{Neem samen} \\ &=-x^2-\frac{25}{6}x-\frac{25}{6} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b-\frac{2}{18})(p-\frac{-2}{8})& =(\color{red}{b}+\color{orange}{\frac{-1}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{4}b-\frac{1}{9}p-\frac{1}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =bp+\frac{1}{4}b-\frac{1}{9}p-\frac{1}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-13}{15}-a)(b-\frac{17}{11})& =(\color{red}{-a}+\color{orange}{\frac{-13}{15}}).(\color{green}{b}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{17}{11}a-\frac{13}{15}b+\frac{13}{15}.\frac{17}{11}& \text{Uitwerken } \\ & =-ab+\frac{17}{11}a-\frac{13}{15}b+\frac{221}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-2}{8})(\frac{6}{9}+b)& =(\color{red}{p}+\color{orange}{\frac{1}{4}}).(\color{green}{b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{3}p+\frac{1}{4}b+\frac{1}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =bp+\frac{2}{3}p+\frac{1}{4}b+\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{3}p+\frac{1}{4}b+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{18}-b)(q+\frac{-4}{7})& =(\color{red}{-b}+\color{orange}{\frac{-7}{9}}).(\color{green}{q}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{4}{7}b-\frac{7}{9}q+\frac{7}{9}.\frac{4}{7}& \text{Uitwerken } \\ & =-bq+\frac{4}{7}b-\frac{7}{9}q+\frac{28}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{4}{7}b-\frac{7}{9}q+\frac{4}{9} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-2}{18})(q-\frac{-14}{8})& =(\color{red}{b}+\color{orange}{\frac{-1}{9}}).(\color{green}{q}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{4}b-\frac{1}{9}q-\frac{1}{9}.\frac{7}{4}& \text{Uitwerken } \\ & =bq+\frac{7}{4}b-\frac{1}{9}q-\frac{7}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{9}{12})(b-\frac{-14}{6})& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{3}p-\frac{3}{4}b-\frac{3}{4}.\frac{7}{3}& \text{Uitwerken } \\ & =bp+\frac{7}{3}p-\frac{3}{4}b-\frac{21}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{7}{3}p-\frac{3}{4}b-\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{15}{5}+b)(\frac{20}{4}-a)& =(\color{red}{b}+\color{orange}{3}).(\color{green}{-a}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(5)} + \color{orange}{(3)} . \color{green}{(-a)} + \color{orange}{(3)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -ab+5b-3a+3.5& \text{Uitwerken } \\ & =-ab+5b-3a+15 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-2}{10})(\frac{2}{5}-x)& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{-x}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{2}{5}x+\frac{1}{5}x-\frac{1}{5}.\frac{2}{5}& \text{Uitwerken } \\ & =-x^2+(\frac{2}{5}+\frac{1}{5})x-\frac{2}{25} & \text{Neem samen} \\ &=-x^2+\frac{3}{5}x-\frac{2}{25} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}((-4)+b)(\frac{-18}{8}-p)& =(\color{red}{b}+\color{orange}{(-4)}).(\color{green}{-p}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(-4)} . \color{green}{(-p)} + \color{orange}{(-4)} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{9}{4}b+4p+4.\frac{9}{4}& \text{Uitwerken } \\ & =-bp-\frac{9}{4}b+4p+\frac{36}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{9}{4}b+4p+9 & \text{Vereenvoudig} \\\end{align}\)
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