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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-11}{10})(b-\frac{-12}{18})& =(\color{red}{a}+\color{orange}{\frac{-11}{10}}).(\color{green}{b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-11}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{3}a-\frac{11}{10}b-\frac{11}{10}.\frac{2}{3}& \text{Uitwerken } \\ & =ab+\frac{2}{3}a-\frac{11}{10}b-\frac{22}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{2}{3}a-\frac{11}{10}b-\frac{11}{15} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{18}{7}-a)(q+\frac{-2}{6})& =(\color{red}{-a}+\color{orange}{\frac{18}{7}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{18}{7})} . \color{green}{(q)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{3}a+\frac{18}{7}q-\frac{18}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =-aq+\frac{1}{3}a+\frac{18}{7}q-\frac{18}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{1}{3}a+\frac{18}{7}q-\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{12}-a)(\frac{5}{10}+q)& =(\color{red}{-a}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{2}a-\frac{4}{3}q-\frac{4}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =-aq-\frac{1}{2}a-\frac{4}{3}q-\frac{4}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{1}{2}a-\frac{4}{3}q-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-13}{10})(\frac{16}{12}+q)& =(\color{red}{a}+\color{orange}{\frac{13}{10}}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{3}a+\frac{13}{10}q+\frac{13}{10}.\frac{4}{3}& \text{Uitwerken } \\ & =aq+\frac{4}{3}a+\frac{13}{10}q+\frac{52}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{4}{3}a+\frac{13}{10}q+\frac{26}{15} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x-\frac{4}{15})(\frac{-16}{11}-q)& =(\color{red}{x}+\color{orange}{\frac{-4}{15}}).(\color{green}{-q}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{16}{11}x+\frac{4}{15}q+\frac{4}{15}.\frac{16}{11}& \text{Uitwerken } \\ & =-qx-\frac{16}{11}x+\frac{4}{15}q+\frac{64}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-11}{7})(\frac{5}{9}+b)& =(\color{red}{p}+\color{orange}{\frac{-11}{7}}).(\color{green}{b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-11}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{9}p-\frac{11}{7}b-\frac{11}{7}.\frac{5}{9}& \text{Uitwerken } \\ & =bp+\frac{5}{9}p-\frac{11}{7}b-\frac{55}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-5}{10}+b)(\frac{-11}{8}+p)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{8}b-\frac{1}{2}p+\frac{1}{2}.\frac{11}{8}& \text{Uitwerken } \\ & =bp-\frac{11}{8}b-\frac{1}{2}p+\frac{11}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{3}{15})(x+\frac{4}{5})& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{4}{5}b+\frac{1}{5}x+\frac{1}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =bx+\frac{4}{5}b+\frac{1}{5}x+\frac{4}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{1}{10}+p)(\frac{13}{16}+x)& =(\color{red}{p}+\color{orange}{\frac{1}{10}}).(\color{green}{x}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{16}p+\frac{1}{10}x+\frac{1}{10}.\frac{13}{16}& \text{Uitwerken } \\ & =px+\frac{13}{16}p+\frac{1}{10}x+\frac{13}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{14}{3}+q)(b-\frac{13}{17})& =(\color{red}{q}+\color{orange}{\frac{14}{3}}).(\color{green}{b}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{14}{3})} . \color{green}{(b)} + \color{orange}{(\frac{14}{3})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{17}q+\frac{14}{3}b-\frac{14}{3}.\frac{13}{17}& \text{Uitwerken } \\ & =bq-\frac{13}{17}q+\frac{14}{3}b-\frac{182}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{7}{8})(\frac{9}{19}-x)& =(\color{red}{b}+\color{orange}{\frac{7}{8}}).(\color{green}{-x}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{7}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{9}{19}b-\frac{7}{8}x+\frac{7}{8}.\frac{9}{19}& \text{Uitwerken } \\ & =-bx+\frac{9}{19}b-\frac{7}{8}x+\frac{63}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-11}{12})(p-\frac{-6}{9})& =(\color{red}{b}+\color{orange}{\frac{11}{12}}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{11}{12})} . \color{green}{(p)} + \color{orange}{(\frac{11}{12})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{3}b+\frac{11}{12}p+\frac{11}{12}.\frac{2}{3}& \text{Uitwerken } \\ & =bp+\frac{2}{3}b+\frac{11}{12}p+\frac{22}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{3}b+\frac{11}{12}p+\frac{11}{18} & \text{Vereenvoudig} \\\end{align}\)
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