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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-16}{5})(\frac{2}{10}-a)& =(\color{red}{q}+\color{orange}{\frac{16}{5}}).(\color{green}{-a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{16}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{5}q-\frac{16}{5}a+\frac{16}{5}.\frac{1}{5}& \text{Uitwerken } \\ & =-aq+\frac{1}{5}q-\frac{16}{5}a+\frac{16}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-13}{15})(\frac{-11}{3}+b)& =(\color{red}{q}+\color{orange}{\frac{-13}{15}}).(\color{green}{b}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{3}q-\frac{13}{15}b+\frac{13}{15}.\frac{11}{3}& \text{Uitwerken } \\ & =bq-\frac{11}{3}q-\frac{13}{15}b+\frac{143}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{7}-q)(q-\frac{9}{14})& =(\color{red}{-q}+\color{orange}{\frac{-16}{7}}).(\color{green}{q}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{9}{14}q-\frac{16}{7}q+\frac{16}{7}.\frac{9}{14}& \text{Uitwerken } \\ & =-q^2+(\frac{9}{14}+(\frac{-16}{7}))q+(\frac{-144}{98}) & \text{Neem samen} \\ &=-q^2-\frac{23}{14}q+(\frac{-144}{98}) & \text{Maak de som} \\ &=-q^2-\frac{23}{14}q+(\frac{-72}{49}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{4}{3}+q)(\frac{-12}{17}-q)& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{-q}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{12}{17}q-\frac{4}{3}q-\frac{4}{3}.\frac{12}{17}& \text{Uitwerken } \\ & =-q^2+((\frac{-12}{17})+(\frac{-4}{3}))q-\frac{48}{51} & \text{Neem samen} \\ &=-q^2-\frac{104}{51}q-\frac{48}{51} & \text{Maak de som} \\ &=-q^2-\frac{104}{51}q-\frac{16}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{12}{9}-q)(\frac{9}{7}+a)& =(\color{red}{-q}+\color{orange}{\frac{4}{3}}).(\color{green}{a}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{9}{7}q+\frac{4}{3}a+\frac{4}{3}.\frac{9}{7}& \text{Uitwerken } \\ & =-aq-\frac{9}{7}q+\frac{4}{3}a+\frac{36}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{9}{7}q+\frac{4}{3}a+\frac{12}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{15}{12})(x-\frac{-12}{19})& =(\color{red}{q}+\color{orange}{\frac{-5}{4}}).(\color{green}{x}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{19}q-\frac{5}{4}x-\frac{5}{4}.\frac{12}{19}& \text{Uitwerken } \\ & =qx+\frac{12}{19}q-\frac{5}{4}x-\frac{60}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{19}q-\frac{5}{4}x-\frac{15}{19} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-20}{13}+a)(x+\frac{-14}{18})& =(\color{red}{a}+\color{orange}{\frac{-20}{13}}).(\color{green}{x}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{9}a-\frac{20}{13}x+\frac{20}{13}.\frac{7}{9}& \text{Uitwerken } \\ & =ax-\frac{7}{9}a-\frac{20}{13}x+\frac{140}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-8}{6})(x+\frac{-18}{13})& =(\color{red}{x}+\color{orange}{\frac{-4}{3}}).(\color{green}{x}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{18}{13}x-\frac{4}{3}x+\frac{4}{3}.\frac{18}{13}& \text{Uitwerken } \\ & =x^2+((\frac{-18}{13})+(\frac{-4}{3}))x+\frac{72}{39} & \text{Neem samen} \\ &=x^2-\frac{106}{39}x+\frac{72}{39} & \text{Maak de som} \\ &=x^2-\frac{106}{39}x+\frac{24}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{16}{2}+x)(\frac{4}{16}-a)& =(\color{red}{x}+\color{orange}{8}).(\color{green}{-a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(8)} . \color{green}{(-a)} + \color{orange}{(8)} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{4}x-8a+8.\frac{1}{4}& \text{Uitwerken } \\ & =-ax+\frac{1}{4}x-8a+\frac{8}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{1}{4}x-8a+2 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x-\frac{18}{9})(q-\frac{6}{17})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{6}{17}x-2q+2.\frac{6}{17}& \text{Uitwerken } \\ & =qx-\frac{6}{17}x-2q+\frac{12}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-10}{3})(x+\frac{-9}{3})& =(\color{red}{b}+\color{orange}{\frac{10}{3}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bx-3b+\frac{10}{3}x-\frac{10}{3}.3& \text{Uitwerken } \\ & =bx-3b+\frac{10}{3}x-\frac{30}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-3b+\frac{10}{3}x-10 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-7}{12}+q)(p-(-14))& =(\color{red}{q}+\color{orange}{\frac{-7}{12}}).(\color{green}{p}+\color{blue}{14})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(14)} + \color{orange}{(\frac{-7}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = pq+14q-\frac{7}{12}p-\frac{7}{12}.14& \text{Uitwerken } \\ & =pq+14q-\frac{7}{12}p-\frac{98}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+14q-\frac{7}{12}p-\frac{49}{6} & \text{Vereenvoudig} \\\end{align}\)
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