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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-5}{14}-q)(p-\frac{-12}{19})& =(\color{red}{-q}+\color{orange}{\frac{-5}{14}}).(\color{green}{p}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{12}{19}q-\frac{5}{14}p-\frac{5}{14}.\frac{12}{19}& \text{Uitwerken } \\ & =-pq-\frac{12}{19}q-\frac{5}{14}p-\frac{60}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{12}{19}q-\frac{5}{14}p-\frac{30}{133} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{4}{16}+b)(a-\frac{19}{13})& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{13}b+\frac{1}{4}a-\frac{1}{4}.\frac{19}{13}& \text{Uitwerken } \\ & =ab-\frac{19}{13}b+\frac{1}{4}a-\frac{19}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{11}{13}-a)(q+\frac{4}{15})& =(\color{red}{-a}+\color{orange}{\frac{11}{13}}).(\color{green}{q}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{11}{13})} . \color{green}{(q)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{4}{15}a+\frac{11}{13}q+\frac{11}{13}.\frac{4}{15}& \text{Uitwerken } \\ & =-aq-\frac{4}{15}a+\frac{11}{13}q+\frac{44}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-18}{17}-x)(\frac{13}{3}-x)& =(\color{red}{-x}+\color{orange}{\frac{-18}{17}}).(\color{green}{-x}+\color{blue}{\frac{13}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{3})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{13}{3})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{13}{3}x+\frac{18}{17}x-\frac{18}{17}.\frac{13}{3}& \text{Uitwerken } \\ & =x^2+((\frac{-13}{3})+\frac{18}{17})x-(\frac{-234}{51}) & \text{Neem samen} \\ &=x^2-\frac{167}{51}x-(\frac{-234}{51}) & \text{Maak de som} \\ &=x^2-\frac{167}{51}x+\frac{78}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{13}+q)(p+\frac{-17}{9})& =(\color{red}{q}+\color{orange}{\frac{5}{13}}).(\color{green}{p}+\color{blue}{\frac{-17}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{9})} + \color{orange}{(\frac{5}{13})} . \color{green}{(p)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{-17}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{9}q+\frac{5}{13}p-\frac{5}{13}.\frac{17}{9}& \text{Uitwerken } \\ & =pq-\frac{17}{9}q+\frac{5}{13}p-\frac{85}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{15}{5})(8-a)& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{-a}+\color{blue}{8})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(-3)} . \color{green}{(-a)} + \color{orange}{(-3)} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = -aa+8a+3a-3.8& \text{Uitwerken } \\ & =-a^2+(8+3)a-24 & \text{Neem samen} \\ &=-a^2+11a-24 & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-2}{2}+q)(\frac{-19}{13}+p)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{13}q-1p+1.\frac{19}{13}& \text{Uitwerken } \\ & =pq-\frac{19}{13}q-1p+\frac{19}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-17}{8}+q)(x-\frac{4}{8})& =(\color{red}{q}+\color{orange}{\frac{-17}{8}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-17}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{2}q-\frac{17}{8}x+\frac{17}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =qx-\frac{1}{2}q-\frac{17}{8}x+\frac{17}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{11}{8})(\frac{3}{14}+a)& =(\color{red}{a}+\color{orange}{\frac{11}{8}}).(\color{green}{a}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{11}{8})} . \color{green}{(a)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{14}a+\frac{11}{8}a+\frac{11}{8}.\frac{3}{14}& \text{Uitwerken } \\ & =a^2+(\frac{3}{14}+\frac{11}{8})a+\frac{33}{112} & \text{Neem samen} \\ &=a^2+\frac{89}{56}a+\frac{33}{112} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-14}{11})(\frac{-2}{13}-p)& =(\color{red}{q}+\color{orange}{\frac{-14}{11}}).(\color{green}{-p}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{13}q+\frac{14}{11}p+\frac{14}{11}.\frac{2}{13}& \text{Uitwerken } \\ & =-pq-\frac{2}{13}q+\frac{14}{11}p+\frac{28}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{6}{11})(\frac{10}{14}-b)& =(\color{red}{p}+\color{orange}{\frac{6}{11}}).(\color{green}{-b}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{6}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{7}p-\frac{6}{11}b+\frac{6}{11}.\frac{5}{7}& \text{Uitwerken } \\ & =-bp+\frac{5}{7}p-\frac{6}{11}b+\frac{30}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{6}{2})(\frac{18}{2}+x)& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{x}+\color{blue}{9})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(9)} + \color{orange}{(-3)} . \color{green}{(x)} + \color{orange}{(-3)} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = bx+9b-3x-3.9& \text{Uitwerken } \\ & =bx+9b-3x-27 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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