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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-13}{11})(\frac{8}{17}+x)& =(\color{red}{x}+\color{orange}{\frac{13}{11}}).(\color{green}{x}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{13}{11})} . \color{green}{(x)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{8}{17}x+\frac{13}{11}x+\frac{13}{11}.\frac{8}{17}& \text{Uitwerken } \\ & =x^2+(\frac{8}{17}+\frac{13}{11})x+\frac{104}{187} & \text{Neem samen} \\ &=x^2+\frac{309}{187}x+\frac{104}{187} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-1}{16})(q+\frac{9}{7})& =(\color{red}{x}+\color{orange}{\frac{1}{16}}).(\color{green}{q}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{1}{16})} . \color{green}{(q)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{7}x+\frac{1}{16}q+\frac{1}{16}.\frac{9}{7}& \text{Uitwerken } \\ & =qx+\frac{9}{7}x+\frac{1}{16}q+\frac{9}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{5}{10})(q-\frac{-12}{13})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{13}x+\frac{1}{2}q+\frac{1}{2}.\frac{12}{13}& \text{Uitwerken } \\ & =qx+\frac{12}{13}x+\frac{1}{2}q+\frac{12}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{13}x+\frac{1}{2}q+\frac{6}{13} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-6}{10}+x)(q+\frac{-17}{6})& =(\color{red}{x}+\color{orange}{\frac{-3}{5}}).(\color{green}{q}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{6}x-\frac{3}{5}q+\frac{3}{5}.\frac{17}{6}& \text{Uitwerken } \\ & =qx-\frac{17}{6}x-\frac{3}{5}q+\frac{51}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{17}{6}x-\frac{3}{5}q+\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p+\frac{8}{20})(\frac{4}{8}-a)& =(\color{red}{p}+\color{orange}{\frac{2}{5}}).(\color{green}{-a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{2}p-\frac{2}{5}a+\frac{2}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-ap+\frac{1}{2}p-\frac{2}{5}a+\frac{2}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{1}{2}p-\frac{2}{5}a+\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-14}{19}-a)(a-\frac{2}{20})& =(\color{red}{-a}+\color{orange}{\frac{-14}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{10}a-\frac{14}{19}a+\frac{14}{19}.\frac{1}{10}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{10}+(\frac{-14}{19}))a+(\frac{-14}{190}) & \text{Neem samen} \\ &=-a^2-\frac{121}{190}a+(\frac{-14}{190}) & \text{Maak de som} \\ &=-a^2-\frac{121}{190}a+(\frac{-7}{95}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-3}{15})(\frac{12}{13}+x)& =(\color{red}{q}+\color{orange}{\frac{1}{5}}).(\color{green}{x}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{13}q+\frac{1}{5}x+\frac{1}{5}.\frac{12}{13}& \text{Uitwerken } \\ & =qx+\frac{12}{13}q+\frac{1}{5}x+\frac{12}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{13}{16})(\frac{-19}{10}+p)& =(\color{red}{b}+\color{orange}{\frac{-13}{16}}).(\color{green}{p}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{10}b-\frac{13}{16}p+\frac{13}{16}.\frac{19}{10}& \text{Uitwerken } \\ & =bp-\frac{19}{10}b-\frac{13}{16}p+\frac{247}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{1}{9}-p)(p-\frac{-6}{10})& =(\color{red}{-p}+\color{orange}{\frac{1}{9}}).(\color{green}{p}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{3}{5}p+\frac{1}{9}p+\frac{1}{9}.\frac{3}{5}& \text{Uitwerken } \\ & =-p^2+((\frac{-3}{5})+\frac{1}{9})p+(\frac{-3}{45}) & \text{Neem samen} \\ &=-p^2-\frac{22}{45}p+(\frac{-3}{45}) & \text{Maak de som} \\ &=-p^2-\frac{22}{45}p+(\frac{-1}{15}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-13}{12}+p)(2+q)& =(\color{red}{p}+\color{orange}{\frac{-13}{12}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-13}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2p-\frac{13}{12}q-\frac{13}{12}.2& \text{Uitwerken } \\ & =pq+2p-\frac{13}{12}q-\frac{26}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+2p-\frac{13}{12}q-\frac{13}{6} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{2}{16})(\frac{20}{9}+a)& =(\color{red}{x}+\color{orange}{\frac{1}{8}}).(\color{green}{a}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{20}{9}x+\frac{1}{8}a+\frac{1}{8}.\frac{20}{9}& \text{Uitwerken } \\ & =ax+\frac{20}{9}x+\frac{1}{8}a+\frac{20}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{20}{9}x+\frac{1}{8}a+\frac{5}{18} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p+\frac{8}{15})(\frac{18}{3}-b)& =(\color{red}{p}+\color{orange}{\frac{8}{15}}).(\color{green}{-b}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(6)} + \color{orange}{(\frac{8}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -bp+6p-\frac{8}{15}b+\frac{8}{15}.6& \text{Uitwerken } \\ & =-bp+6p-\frac{8}{15}b+\frac{48}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+6p-\frac{8}{15}b+\frac{16}{5} & \text{Vereenvoudig} \\\end{align}\)
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