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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{-4}{8})(x+\frac{10}{15})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{2}{3}x-\frac{1}{2}x-\frac{1}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =x^2+(\frac{2}{3}+(\frac{-1}{2}))x-(\frac{-2}{6}) & \text{Neem samen} \\ &=x^2+\frac{1}{6}x-(\frac{-2}{6}) & \text{Maak de som} \\ &=x^2+\frac{1}{6}x+\frac{1}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(\frac{-10}{15}-b)(x+\frac{-11}{8})& =(\color{red}{-b}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{11}{8}b-\frac{2}{3}x+\frac{2}{3}.\frac{11}{8}& \text{Uitwerken } \\ & =-bx+\frac{11}{8}b-\frac{2}{3}x+\frac{22}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{11}{8}b-\frac{2}{3}x+\frac{11}{12} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-17}{6})(b-\frac{-7}{15})& =(\color{red}{x}+\color{orange}{\frac{-17}{6}}).(\color{green}{b}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{15}x-\frac{17}{6}b-\frac{17}{6}.\frac{7}{15}& \text{Uitwerken } \\ & =bx+\frac{7}{15}x-\frac{17}{6}b-\frac{119}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-12}{18})(p+\frac{15}{17})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{15}{17}p+\frac{2}{3}p+\frac{2}{3}.\frac{15}{17}& \text{Uitwerken } \\ & =p^2+(\frac{15}{17}+\frac{2}{3})p+\frac{30}{51} & \text{Neem samen} \\ &=p^2+\frac{79}{51}p+\frac{30}{51} & \text{Maak de som} \\ &=p^2+\frac{79}{51}p+\frac{10}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(b+\frac{-13}{20})(x+\frac{7}{16})& =(\color{red}{b}+\color{orange}{\frac{-13}{20}}).(\color{green}{x}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{16}b-\frac{13}{20}x-\frac{13}{20}.\frac{7}{16}& \text{Uitwerken } \\ & =bx+\frac{7}{16}b-\frac{13}{20}x-\frac{91}{320} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{17}{12}-p)(x-\frac{6}{17})& =(\color{red}{-p}+\color{orange}{\frac{17}{12}}).(\color{green}{x}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{17}{12})} . \color{green}{(x)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{6}{17}p+\frac{17}{12}x-\frac{17}{12}.\frac{6}{17}& \text{Uitwerken } \\ & =-px+\frac{6}{17}p+\frac{17}{12}x-\frac{102}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{6}{17}p+\frac{17}{12}x-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-4}{6})(\frac{17}{16}-x)& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{-x}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{17}{16}p-\frac{2}{3}x+\frac{2}{3}.\frac{17}{16}& \text{Uitwerken } \\ & =-px+\frac{17}{16}p-\frac{2}{3}x+\frac{34}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{17}{16}p-\frac{2}{3}x+\frac{17}{24} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{11}{19}+x)(\frac{20}{6}-a)& =(\color{red}{x}+\color{orange}{\frac{11}{19}}).(\color{green}{-a}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{11}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{10}{3}x-\frac{11}{19}a+\frac{11}{19}.\frac{10}{3}& \text{Uitwerken } \\ & =-ax+\frac{10}{3}x-\frac{11}{19}a+\frac{110}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{14}{3}+x)(\frac{5}{6}-q)& =(\color{red}{x}+\color{orange}{\frac{14}{3}}).(\color{green}{-q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{14}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{14}{3})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{6}x-\frac{14}{3}q+\frac{14}{3}.\frac{5}{6}& \text{Uitwerken } \\ & =-qx+\frac{5}{6}x-\frac{14}{3}q+\frac{70}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{5}{6}x-\frac{14}{3}q+\frac{35}{9} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{17}{8}-x)(\frac{-15}{5}-p)& =(\color{red}{-x}+\color{orange}{\frac{17}{8}}).(\color{green}{-p}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{17}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = px+3x-\frac{17}{8}p-\frac{17}{8}.3& \text{Uitwerken } \\ & =px+3x-\frac{17}{8}p-\frac{51}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{3}{13})(p+\frac{18}{9})& =(\color{red}{x}+\color{orange}{\frac{3}{13}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{3}{13})} . \color{green}{(p)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = px+2x+\frac{3}{13}p+\frac{3}{13}.2& \text{Uitwerken } \\ & =px+2x+\frac{3}{13}p+\frac{6}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{3}+b)(\frac{12}{7}-a)& =(\color{red}{b}+\color{orange}{\frac{13}{3}}).(\color{green}{-a}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{13}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{12}{7}b-\frac{13}{3}a+\frac{13}{3}.\frac{12}{7}& \text{Uitwerken } \\ & =-ab+\frac{12}{7}b-\frac{13}{3}a+\frac{156}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{12}{7}b-\frac{13}{3}a+\frac{52}{7} & \text{Vereenvoudig} \\\end{align}\)
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