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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{12}{4}+b)(a+\frac{-2}{7})& =(\color{red}{b}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{7}b+3a-3.\frac{2}{7}& \text{Uitwerken } \\ & =ab-\frac{2}{7}b+3a-\frac{6}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-17}{19}+x)(\frac{-7}{19}+a)& =(\color{red}{x}+\color{orange}{\frac{-17}{19}}).(\color{green}{a}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{19}x-\frac{17}{19}a+\frac{17}{19}.\frac{7}{19}& \text{Uitwerken } \\ & =ax-\frac{7}{19}x-\frac{17}{19}a+\frac{119}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{18}{18})(a-\frac{2}{6})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{3}q+1a-1.\frac{1}{3}& \text{Uitwerken } \\ & =aq-\frac{1}{3}q+1a-\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{10}-p)(\frac{4}{17}+x)& =(\color{red}{-p}+\color{orange}{\frac{11}{10}}).(\color{green}{x}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{11}{10})} . \color{green}{(x)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{4}{17}p+\frac{11}{10}x+\frac{11}{10}.\frac{4}{17}& \text{Uitwerken } \\ & =-px-\frac{4}{17}p+\frac{11}{10}x+\frac{44}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{4}{17}p+\frac{11}{10}x+\frac{22}{85} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{6}-a)(x-\frac{20}{19})& =(\color{red}{-a}+\color{orange}{\frac{5}{3}}).(\color{green}{x}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{20}{19}a+\frac{5}{3}x-\frac{5}{3}.\frac{20}{19}& \text{Uitwerken } \\ & =-ax+\frac{20}{19}a+\frac{5}{3}x-\frac{100}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{20}{16})(\frac{-5}{16}-x)& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{-x}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{5}{16}p+\frac{5}{4}x+\frac{5}{4}.\frac{5}{16}& \text{Uitwerken } \\ & =-px-\frac{5}{16}p+\frac{5}{4}x+\frac{25}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-6}{10})(\frac{19}{10}+q)& =(\color{red}{a}+\color{orange}{\frac{3}{5}}).(\color{green}{q}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{10}a+\frac{3}{5}q+\frac{3}{5}.\frac{19}{10}& \text{Uitwerken } \\ & =aq+\frac{19}{10}a+\frac{3}{5}q+\frac{57}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{2}{12})(a+\frac{4}{5})& =(\color{red}{x}+\color{orange}{\frac{1}{6}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{5}x+\frac{1}{6}a+\frac{1}{6}.\frac{4}{5}& \text{Uitwerken } \\ & =ax+\frac{4}{5}x+\frac{1}{6}a+\frac{4}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{4}{5}x+\frac{1}{6}a+\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-11}{2})(a-\frac{19}{16})& =(\color{red}{a}+\color{orange}{\frac{11}{2}}).(\color{green}{a}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{11}{2})} . \color{green}{(a)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{19}{16}a+\frac{11}{2}a-\frac{11}{2}.\frac{19}{16}& \text{Uitwerken } \\ & =a^2+((\frac{-19}{16})+\frac{11}{2})a-(\frac{-209}{32}) & \text{Neem samen} \\ &=a^2+\frac{69}{16}a-(\frac{-209}{32}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{4}{16}-b)(b+\frac{3}{14})& =(\color{red}{-b}+\color{orange}{\frac{1}{4}}).(\color{green}{b}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{3}{14}b+\frac{1}{4}b+\frac{1}{4}.\frac{3}{14}& \text{Uitwerken } \\ & =-b^2+((\frac{-3}{14})+\frac{1}{4})b+(\frac{-3}{56}) & \text{Neem samen} \\ &=-b^2+\frac{1}{28}b+(\frac{-3}{56}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{1}{8}+x)(\frac{7}{3}+q)& =(\color{red}{x}+\color{orange}{\frac{1}{8}}).(\color{green}{q}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{1}{8})} . \color{green}{(q)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{3}x+\frac{1}{8}q+\frac{1}{8}.\frac{7}{3}& \text{Uitwerken } \\ & =qx+\frac{7}{3}x+\frac{1}{8}q+\frac{7}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{13}{8})(p+\frac{15}{14})& =(\color{red}{p}+\color{orange}{\frac{-13}{8}}).(\color{green}{p}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{15}{14}p-\frac{13}{8}p-\frac{13}{8}.\frac{15}{14}& \text{Uitwerken } \\ & =p^2+(\frac{15}{14}+(\frac{-13}{8}))p-(\frac{-195}{112}) & \text{Neem samen} \\ &=p^2-\frac{31}{56}p-(\frac{-195}{112}) & \text{Maak de som} \\\end{align}\)
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