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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{13}-p)(x+\frac{17}{13})& =(\color{red}{-p}+\color{orange}{\frac{11}{13}}).(\color{green}{x}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{11}{13})} . \color{green}{(x)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{17}{13}p+\frac{11}{13}x+\frac{11}{13}.\frac{17}{13}& \text{Uitwerken } \\ & =-px-\frac{17}{13}p+\frac{11}{13}x+\frac{187}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-3}{7})(p+\frac{4}{8})& =(\color{red}{x}+\color{orange}{\frac{3}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{2}x+\frac{3}{7}p+\frac{3}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =px+\frac{1}{2}x+\frac{3}{7}p+\frac{3}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-11}{4})(\frac{16}{20}+a)& =(\color{red}{p}+\color{orange}{\frac{11}{4}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{11}{4})} . \color{green}{(a)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{5}p+\frac{11}{4}a+\frac{11}{4}.\frac{4}{5}& \text{Uitwerken } \\ & =ap+\frac{4}{5}p+\frac{11}{4}a+\frac{44}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{4}{5}p+\frac{11}{4}a+\frac{11}{5} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{19}{2}-p)(\frac{-2}{3}+x)& =(\color{red}{-p}+\color{orange}{\frac{19}{2}}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{19}{2})} . \color{green}{(x)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{3}p+\frac{19}{2}x-\frac{19}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =-px+\frac{2}{3}p+\frac{19}{2}x-\frac{38}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{2}{3}p+\frac{19}{2}x-\frac{19}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{17}+x)(\frac{-18}{2}-q)& =(\color{red}{x}+\color{orange}{\frac{-10}{17}}).(\color{green}{-q}+\color{blue}{(-9)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(-9)} + \color{orange}{(\frac{-10}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -qx-9x+\frac{10}{17}q+\frac{10}{17}.9& \text{Uitwerken } \\ & =-qx-9x+\frac{10}{17}q+\frac{90}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{13}{2})(\frac{-14}{15}+p)& =(\color{red}{b}+\color{orange}{\frac{13}{2}}).(\color{green}{p}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{13}{2})} . \color{green}{(p)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{14}{15}b+\frac{13}{2}p-\frac{13}{2}.\frac{14}{15}& \text{Uitwerken } \\ & =bp-\frac{14}{15}b+\frac{13}{2}p-\frac{182}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{14}{15}b+\frac{13}{2}p-\frac{91}{15} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{15}{9}+b)(x+\frac{-18}{17})& =(\color{red}{b}+\color{orange}{\frac{5}{3}}).(\color{green}{x}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{18}{17}b+\frac{5}{3}x-\frac{5}{3}.\frac{18}{17}& \text{Uitwerken } \\ & =bx-\frac{18}{17}b+\frac{5}{3}x-\frac{90}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{18}{17}b+\frac{5}{3}x-\frac{30}{17} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a-\frac{14}{8})(b-\frac{-13}{20})& =(\color{red}{a}+\color{orange}{\frac{-7}{4}}).(\color{green}{b}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{20}a-\frac{7}{4}b-\frac{7}{4}.\frac{13}{20}& \text{Uitwerken } \\ & =ab+\frac{13}{20}a-\frac{7}{4}b-\frac{91}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-7}{3})(x+\frac{11}{9})& =(\color{red}{a}+\color{orange}{\frac{-7}{3}}).(\color{green}{x}+\color{blue}{\frac{11}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{9})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{11}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{9}a-\frac{7}{3}x-\frac{7}{3}.\frac{11}{9}& \text{Uitwerken } \\ & =ax+\frac{11}{9}a-\frac{7}{3}x-\frac{77}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-1}{5})(\frac{6}{10}+x)& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{x}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{5}b+\frac{1}{5}x+\frac{1}{5}.\frac{3}{5}& \text{Uitwerken } \\ & =bx+\frac{3}{5}b+\frac{1}{5}x+\frac{3}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-7}{10})(p-\frac{14}{20})& =(\color{red}{q}+\color{orange}{\frac{-7}{10}}).(\color{green}{p}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{10}q-\frac{7}{10}p+\frac{7}{10}.\frac{7}{10}& \text{Uitwerken } \\ & =pq-\frac{7}{10}q-\frac{7}{10}p+\frac{49}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-20}{16}-x)(10-q)& =(\color{red}{-x}+\color{orange}{\frac{-5}{4}}).(\color{green}{-q}+\color{blue}{10})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(10)} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = qx-10x+\frac{5}{4}q-\frac{5}{4}.10& \text{Uitwerken } \\ & =qx-10x+\frac{5}{4}q-\frac{50}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-10x+\frac{5}{4}q-\frac{25}{2} & \text{Vereenvoudig} \\\end{align}\)
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