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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{20}{17})(q-\frac{-12}{3})& =(\color{red}{x}+\color{orange}{\frac{-20}{17}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(4)} + \color{orange}{(\frac{-20}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = qx+4x-\frac{20}{17}q-\frac{20}{17}.4& \text{Uitwerken } \\ & =qx+4x-\frac{20}{17}q-\frac{80}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{4}{13}-x)(b+\frac{-18}{6})& =(\color{red}{-x}+\color{orange}{\frac{4}{13}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{4}{13})} . \color{green}{(b)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bx+3x+\frac{4}{13}b-\frac{4}{13}.3& \text{Uitwerken } \\ & =-bx+3x+\frac{4}{13}b-\frac{12}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{4}{13})(\frac{-19}{6}+b)& =(\color{red}{a}+\color{orange}{\frac{-4}{13}}).(\color{green}{b}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{6}a-\frac{4}{13}b+\frac{4}{13}.\frac{19}{6}& \text{Uitwerken } \\ & =ab-\frac{19}{6}a-\frac{4}{13}b+\frac{76}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{19}{6}a-\frac{4}{13}b+\frac{38}{39} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{4}{4}-x)(\frac{-18}{5}+q)& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{18}{5}x+1q-1.\frac{18}{5}& \text{Uitwerken } \\ & =-qx+\frac{18}{5}x+1q-\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(16-b)(a-\frac{-9}{7})& =(\color{red}{-b}+\color{orange}{16}).(\color{green}{a}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(16)} . \color{green}{(a)} + \color{orange}{(16)} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{9}{7}b+16a+16.\frac{9}{7}& \text{Uitwerken } \\ & =-ab-\frac{9}{7}b+16a+\frac{144}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{7}{9}+q)(b+\frac{-16}{10})& =(\color{red}{q}+\color{orange}{\frac{7}{9}}).(\color{green}{b}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{7}{9})} . \color{green}{(b)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{5}q+\frac{7}{9}b-\frac{7}{9}.\frac{8}{5}& \text{Uitwerken } \\ & =bq-\frac{8}{5}q+\frac{7}{9}b-\frac{56}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{-6}{12})(x-\frac{15}{17})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{15}{17}x-\frac{1}{2}x+\frac{1}{2}.\frac{15}{17}& \text{Uitwerken } \\ & =x^2+((\frac{-15}{17})+(\frac{-1}{2}))x+\frac{15}{34} & \text{Neem samen} \\ &=x^2-\frac{47}{34}x+\frac{15}{34} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{5}-q)(\frac{-9}{19}+b)& =(\color{red}{-q}+\color{orange}{\frac{18}{5}}).(\color{green}{b}+\color{blue}{\frac{-9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{19})} + \color{orange}{(\frac{18}{5})} . \color{green}{(b)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{-9}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{9}{19}q+\frac{18}{5}b-\frac{18}{5}.\frac{9}{19}& \text{Uitwerken } \\ & =-bq+\frac{9}{19}q+\frac{18}{5}b-\frac{162}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-14}{18}+q)(\frac{-15}{17}+q)& =(\color{red}{q}+\color{orange}{\frac{-7}{9}}).(\color{green}{q}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{15}{17}q-\frac{7}{9}q+\frac{7}{9}.\frac{15}{17}& \text{Uitwerken } \\ & =q^2+((\frac{-15}{17})+(\frac{-7}{9}))q+\frac{105}{153} & \text{Neem samen} \\ &=q^2-\frac{254}{153}q+\frac{105}{153} & \text{Maak de som} \\ &=q^2-\frac{254}{153}q+\frac{35}{51} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{13}{11}+q)(\frac{-10}{6}-a)& =(\color{red}{q}+\color{orange}{\frac{13}{11}}).(\color{green}{-a}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{13}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{3}q-\frac{13}{11}a-\frac{13}{11}.\frac{5}{3}& \text{Uitwerken } \\ & =-aq-\frac{5}{3}q-\frac{13}{11}a-\frac{65}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-17}{16}+b)(b-\frac{-13}{9})& =(\color{red}{b}+\color{orange}{\frac{-17}{16}}).(\color{green}{b}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{13}{9}b-\frac{17}{16}b-\frac{17}{16}.\frac{13}{9}& \text{Uitwerken } \\ & =b^2+(\frac{13}{9}+(\frac{-17}{16}))b-(\frac{-221}{144}) & \text{Neem samen} \\ &=b^2+\frac{55}{144}b-(\frac{-221}{144}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q+\frac{7}{15})(q+\frac{-13}{8})& =(\color{red}{q}+\color{orange}{\frac{7}{15}}).(\color{green}{q}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{7}{15})} . \color{green}{(q)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{13}{8}q+\frac{7}{15}q-\frac{7}{15}.\frac{13}{8}& \text{Uitwerken } \\ & =q^2+((\frac{-13}{8})+\frac{7}{15})q-(\frac{-91}{120}) & \text{Neem samen} \\ &=q^2-\frac{139}{120}q-(\frac{-91}{120}) & \text{Maak de som} \\\end{align}\)
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