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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{9}-a)(\frac{20}{12}+a)& =(\color{red}{-a}+\color{orange}{\frac{20}{9}}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{20}{9})} . \color{green}{(a)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{5}{3}a+\frac{20}{9}a+\frac{20}{9}.\frac{5}{3}& \text{Uitwerken } \\ & =-a^2+((\frac{-5}{3})+\frac{20}{9})a+(\frac{-100}{27}) & \text{Neem samen} \\ &=-a^2+\frac{5}{9}a+(\frac{-100}{27}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(15+a)(\frac{-11}{5}+x)& =(\color{red}{a}+\color{orange}{15}).(\color{green}{x}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(15)} . \color{green}{(x)} + \color{orange}{(15)} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{5}a+15x-15.\frac{11}{5}& \text{Uitwerken } \\ & =ax-\frac{11}{5}a+15x-\frac{165}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{11}{5}a+15x-33 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-14}{5})(\frac{9}{8}+x)& =(\color{red}{b}+\color{orange}{\frac{14}{5}}).(\color{green}{x}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{14}{5})} . \color{green}{(x)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{8}b+\frac{14}{5}x+\frac{14}{5}.\frac{9}{8}& \text{Uitwerken } \\ & =bx+\frac{9}{8}b+\frac{14}{5}x+\frac{126}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{9}{8}b+\frac{14}{5}x+\frac{63}{20} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-15}{14})(\frac{11}{10}-p)& =(\color{red}{x}+\color{orange}{\frac{-15}{14}}).(\color{green}{-p}+\color{blue}{\frac{11}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{11}{10})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{11}{10})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{11}{10}x+\frac{15}{14}p-\frac{15}{14}.\frac{11}{10}& \text{Uitwerken } \\ & =-px+\frac{11}{10}x+\frac{15}{14}p-\frac{165}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{11}{10}x+\frac{15}{14}p-\frac{33}{28} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q-\frac{9}{6})(b+\frac{9}{3})& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bq+3q-\frac{3}{2}b-\frac{3}{2}.3& \text{Uitwerken } \\ & =bq+3q-\frac{3}{2}b-\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{10}{10}+p)(\frac{-3}{17}-p)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{3}{17}p-1p-1.\frac{3}{17}& \text{Uitwerken } \\ & =-p^2+((\frac{-3}{17})+(-1))p-\frac{3}{17} & \text{Neem samen} \\ &=-p^2-\frac{20}{17}p-\frac{3}{17} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-18}{9})(\frac{1}{6}+b)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{6}q-2b-2.\frac{1}{6}& \text{Uitwerken } \\ & =bq+\frac{1}{6}q-2b-\frac{2}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{1}{6}q-2b-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-11}{8})(q-\frac{15}{2})& =(\color{red}{p}+\color{orange}{\frac{11}{8}}).(\color{green}{q}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{11}{8})} . \color{green}{(q)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{15}{2}p+\frac{11}{8}q-\frac{11}{8}.\frac{15}{2}& \text{Uitwerken } \\ & =pq-\frac{15}{2}p+\frac{11}{8}q-\frac{165}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{11}{3}+q)(2-x)& =(\color{red}{q}+\color{orange}{\frac{11}{3}}).(\color{green}{-x}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{11}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qx+2q-\frac{11}{3}x+\frac{11}{3}.2& \text{Uitwerken } \\ & =-qx+2q-\frac{11}{3}x+\frac{22}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-19}{3})(a-\frac{-18}{16})& =(\color{red}{q}+\color{orange}{\frac{19}{3}}).(\color{green}{a}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{19}{3})} . \color{green}{(a)} + \color{orange}{(\frac{19}{3})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{8}q+\frac{19}{3}a+\frac{19}{3}.\frac{9}{8}& \text{Uitwerken } \\ & =aq+\frac{9}{8}q+\frac{19}{3}a+\frac{171}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{9}{8}q+\frac{19}{3}a+\frac{57}{8} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{9}{11})(x+\frac{19}{13})& =(\color{red}{x}+\color{orange}{\frac{-9}{11}}).(\color{green}{x}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{19}{13}x-\frac{9}{11}x-\frac{9}{11}.\frac{19}{13}& \text{Uitwerken } \\ & =x^2+(\frac{19}{13}+(\frac{-9}{11}))x-(\frac{-171}{143}) & \text{Neem samen} \\ &=x^2+\frac{92}{143}x-(\frac{-171}{143}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-8}{10}+p)(q+\frac{16}{2})& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{q}+\color{blue}{8})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(8)} + \color{orange}{(\frac{-4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = pq+8p-\frac{4}{5}q-\frac{4}{5}.8& \text{Uitwerken } \\ & =pq+8p-\frac{4}{5}q-\frac{32}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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