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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-8}{5})(q+\frac{10}{14})& =(\color{red}{a}+\color{orange}{\frac{-8}{5}}).(\color{green}{q}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{7}a-\frac{8}{5}q-\frac{8}{5}.\frac{5}{7}& \text{Uitwerken } \\ & =aq+\frac{5}{7}a-\frac{8}{5}q-\frac{40}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{5}{7}a-\frac{8}{5}q-\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{11}{5}+p)(\frac{4}{10}-q)& =(\color{red}{p}+\color{orange}{\frac{11}{5}}).(\color{green}{-q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{11}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{2}{5}p-\frac{11}{5}q+\frac{11}{5}.\frac{2}{5}& \text{Uitwerken } \\ & =-pq+\frac{2}{5}p-\frac{11}{5}q+\frac{22}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{12}+p)(q+\frac{-11}{8})& =(\color{red}{p}+\color{orange}{\frac{-11}{12}}).(\color{green}{q}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{8}p-\frac{11}{12}q+\frac{11}{12}.\frac{11}{8}& \text{Uitwerken } \\ & =pq-\frac{11}{8}p-\frac{11}{12}q+\frac{121}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-4}{11})(\frac{4}{17}-x)& =(\color{red}{q}+\color{orange}{\frac{-4}{11}}).(\color{green}{-x}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{-4}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{4}{17}q+\frac{4}{11}x-\frac{4}{11}.\frac{4}{17}& \text{Uitwerken } \\ & =-qx+\frac{4}{17}q+\frac{4}{11}x-\frac{16}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{13}+a)(\frac{15}{18}-b)& =(\color{red}{a}+\color{orange}{\frac{-9}{13}}).(\color{green}{-b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{6}a+\frac{9}{13}b-\frac{9}{13}.\frac{5}{6}& \text{Uitwerken } \\ & =-ab+\frac{5}{6}a+\frac{9}{13}b-\frac{45}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{6}a+\frac{9}{13}b-\frac{15}{26} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{4}{10}-a)(x+\frac{9}{6})& =(\color{red}{-a}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{2}a+\frac{2}{5}x+\frac{2}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =-ax-\frac{3}{2}a+\frac{2}{5}x+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{3}{2}a+\frac{2}{5}x+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-4}{10}+x)(a-\frac{4}{19})& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{19}x-\frac{2}{5}a+\frac{2}{5}.\frac{4}{19}& \text{Uitwerken } \\ & =ax-\frac{4}{19}x-\frac{2}{5}a+\frac{8}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-17}{8})(a+\frac{4}{3})& =(\color{red}{p}+\color{orange}{\frac{17}{8}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{17}{8})} . \color{green}{(a)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{3}p+\frac{17}{8}a+\frac{17}{8}.\frac{4}{3}& \text{Uitwerken } \\ & =ap+\frac{4}{3}p+\frac{17}{8}a+\frac{68}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{4}{3}p+\frac{17}{8}a+\frac{17}{6} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-4}{6})(x-\frac{-13}{12})& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{13}{12}a+\frac{2}{3}x+\frac{2}{3}.\frac{13}{12}& \text{Uitwerken } \\ & =ax+\frac{13}{12}a+\frac{2}{3}x+\frac{26}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{13}{12}a+\frac{2}{3}x+\frac{13}{18} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b+\frac{20}{11})(\frac{17}{12}+b)& =(\color{red}{b}+\color{orange}{\frac{20}{11}}).(\color{green}{b}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{20}{11})} . \color{green}{(b)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{17}{12}b+\frac{20}{11}b+\frac{20}{11}.\frac{17}{12}& \text{Uitwerken } \\ & =b^2+(\frac{17}{12}+\frac{20}{11})b+\frac{340}{132} & \text{Neem samen} \\ &=b^2+\frac{427}{132}b+\frac{340}{132} & \text{Maak de som} \\ &=b^2+\frac{427}{132}b+\frac{85}{33} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{6}+q)(p-\frac{2}{5})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{5}q+\frac{2}{3}p-\frac{2}{3}.\frac{2}{5}& \text{Uitwerken } \\ & =pq-\frac{2}{5}q+\frac{2}{3}p-\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{12}{3}+p)(p+\frac{13}{16})& =(\color{red}{p}+\color{orange}{4}).(\color{green}{p}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{13}{16}p+4p+4.\frac{13}{16}& \text{Uitwerken } \\ & =p^2+(\frac{13}{16}+4)p+\frac{52}{16} & \text{Neem samen} \\ &=p^2+\frac{77}{16}p+\frac{52}{16} & \text{Maak de som} \\ &=p^2+\frac{77}{16}p+\frac{13}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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