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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{3}{7}-p)(x+\frac{19}{4})& =(\color{red}{-p}+\color{orange}{\frac{3}{7}}).(\color{green}{x}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{3}{7})} . \color{green}{(x)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{4}p+\frac{3}{7}x+\frac{3}{7}.\frac{19}{4}& \text{Uitwerken } \\ & =-px-\frac{19}{4}p+\frac{3}{7}x+\frac{57}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-9)(\frac{-1}{11}-b)& =(\color{red}{x}+\color{orange}{(-9)}).(\color{green}{-b}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(-9)} . \color{green}{(-b)} + \color{orange}{(-9)} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{11}x+9b+9.\frac{1}{11}& \text{Uitwerken } \\ & =-bx-\frac{1}{11}x+9b+\frac{9}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{12}{8})(\frac{11}{4}-x)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{-x}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{11}{4}a-\frac{3}{2}x+\frac{3}{2}.\frac{11}{4}& \text{Uitwerken } \\ & =-ax+\frac{11}{4}a-\frac{3}{2}x+\frac{33}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{3}{20}+q)(\frac{-13}{16}+x)& =(\color{red}{q}+\color{orange}{\frac{3}{20}}).(\color{green}{x}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{3}{20})} . \color{green}{(x)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{16}q+\frac{3}{20}x-\frac{3}{20}.\frac{13}{16}& \text{Uitwerken } \\ & =qx-\frac{13}{16}q+\frac{3}{20}x-\frac{39}{320} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{9}-b)(p-\frac{2}{5})& =(\color{red}{-b}+\color{orange}{\frac{16}{9}}).(\color{green}{p}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{16}{9})} . \color{green}{(p)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{2}{5}b+\frac{16}{9}p-\frac{16}{9}.\frac{2}{5}& \text{Uitwerken } \\ & =-bp+\frac{2}{5}b+\frac{16}{9}p-\frac{32}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{2}{8}-b)(\frac{-17}{12}+p)& =(\color{red}{-b}+\color{orange}{\frac{1}{4}}).(\color{green}{p}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{17}{12}b+\frac{1}{4}p-\frac{1}{4}.\frac{17}{12}& \text{Uitwerken } \\ & =-bp+\frac{17}{12}b+\frac{1}{4}p-\frac{17}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-11}{19}-b)(\frac{9}{13}-a)& =(\color{red}{-b}+\color{orange}{\frac{-11}{19}}).(\color{green}{-a}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{13}b+\frac{11}{19}a-\frac{11}{19}.\frac{9}{13}& \text{Uitwerken } \\ & =ab-\frac{9}{13}b+\frac{11}{19}a-\frac{99}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{19}{8}+p)(\frac{-11}{12}+p)& =(\color{red}{p}+\color{orange}{\frac{19}{8}}).(\color{green}{p}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{19}{8})} . \color{green}{(p)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{11}{12}p+\frac{19}{8}p-\frac{19}{8}.\frac{11}{12}& \text{Uitwerken } \\ & =p^2+((\frac{-11}{12})+\frac{19}{8})p-(\frac{-209}{96}) & \text{Neem samen} \\ &=p^2+\frac{35}{24}p-(\frac{-209}{96}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{15}+x)(x+\frac{6}{12})& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{2}x+\frac{2}{5}x+\frac{2}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =x^2+(\frac{1}{2}+\frac{2}{5})x+\frac{2}{10} & \text{Neem samen} \\ &=x^2+\frac{9}{10}x+\frac{2}{10} & \text{Maak de som} \\ &=x^2+\frac{9}{10}x+\frac{1}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-6}{6}-x)(b-\frac{7}{9})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{9}x-1b+1.\frac{7}{9}& \text{Uitwerken } \\ & =-bx+\frac{7}{9}x-1b+\frac{7}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-5}{15}+b)(a+(-2))& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ab-2b-\frac{1}{3}a+\frac{1}{3}.2& \text{Uitwerken } \\ & =ab-2b-\frac{1}{3}a+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{2}{16}+a)(\frac{-12}{17}-b)& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{-b}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{12}{17}a-\frac{1}{8}b-\frac{1}{8}.\frac{12}{17}& \text{Uitwerken } \\ & =-ab-\frac{12}{17}a-\frac{1}{8}b-\frac{12}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{12}{17}a-\frac{1}{8}b-\frac{3}{34} & \text{Vereenvoudig} \\\end{align}\)
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