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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-15}{4}-a)(\frac{20}{14}-x)& =(\color{red}{-a}+\color{orange}{\frac{-15}{4}}).(\color{green}{-x}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{10}{7}a+\frac{15}{4}x-\frac{15}{4}.\frac{10}{7}& \text{Uitwerken } \\ & =ax-\frac{10}{7}a+\frac{15}{4}x-\frac{150}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{10}{7}a+\frac{15}{4}x-\frac{75}{14} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-10}{14}+q)(a-\frac{-19}{3})& =(\color{red}{q}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{3}q-\frac{5}{7}a-\frac{5}{7}.\frac{19}{3}& \text{Uitwerken } \\ & =aq+\frac{19}{3}q-\frac{5}{7}a-\frac{95}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-20}{15}-b)(p-\frac{-19}{11})& =(\color{red}{-b}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{19}{11}b-\frac{4}{3}p-\frac{4}{3}.\frac{19}{11}& \text{Uitwerken } \\ & =-bp-\frac{19}{11}b-\frac{4}{3}p-\frac{76}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-18}{17}+x)(\frac{-17}{2}+a)& =(\color{red}{x}+\color{orange}{\frac{-18}{17}}).(\color{green}{a}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{2}x-\frac{18}{17}a+\frac{18}{17}.\frac{17}{2}& \text{Uitwerken } \\ & =ax-\frac{17}{2}x-\frac{18}{17}a+\frac{306}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{17}{2}x-\frac{18}{17}a+9 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-19}{5})(\frac{10}{14}-a)& =(\color{red}{x}+\color{orange}{\frac{-19}{5}}).(\color{green}{-a}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{7}x+\frac{19}{5}a-\frac{19}{5}.\frac{5}{7}& \text{Uitwerken } \\ & =-ax+\frac{5}{7}x+\frac{19}{5}a-\frac{95}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{5}{7}x+\frac{19}{5}a-\frac{19}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-18}{11})(b+\frac{-7}{15})& =(\color{red}{x}+\color{orange}{\frac{-18}{11}}).(\color{green}{b}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{-18}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-18}{11})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{15}x-\frac{18}{11}b+\frac{18}{11}.\frac{7}{15}& \text{Uitwerken } \\ & =bx-\frac{7}{15}x-\frac{18}{11}b+\frac{126}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{7}{15}x-\frac{18}{11}b+\frac{42}{55} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+\frac{13}{17})(\frac{12}{2}+b)& =(\color{red}{p}+\color{orange}{\frac{13}{17}}).(\color{green}{b}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(6)} + \color{orange}{(\frac{13}{17})} . \color{green}{(b)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bp+6p+\frac{13}{17}b+\frac{13}{17}.6& \text{Uitwerken } \\ & =bp+6p+\frac{13}{17}b+\frac{78}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+(-1))(\frac{-6}{13}-x)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{6}{13}a+1x+1.\frac{6}{13}& \text{Uitwerken } \\ & =-ax-\frac{6}{13}a+1x+\frac{6}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{-5}{20})(x+\frac{-10}{19})& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{x}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{10}{19}q-\frac{1}{4}x+\frac{1}{4}.\frac{10}{19}& \text{Uitwerken } \\ & =qx-\frac{10}{19}q-\frac{1}{4}x+\frac{10}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{10}{19}q-\frac{1}{4}x+\frac{5}{38} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-12}{16}-x)(\frac{-8}{18}-b)& =(\color{red}{-x}+\color{orange}{\frac{-3}{4}}).(\color{green}{-b}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{4}{9}x+\frac{3}{4}b+\frac{3}{4}.\frac{4}{9}& \text{Uitwerken } \\ & =bx+\frac{4}{9}x+\frac{3}{4}b+\frac{12}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{4}{9}x+\frac{3}{4}b+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{2}{5}+x)(\frac{-10}{10}+x)& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = xx-1x+\frac{2}{5}x-\frac{2}{5}.1& \text{Uitwerken } \\ & =x^2+((-1)+\frac{2}{5})x-(\frac{-2}{5}) & \text{Neem samen} \\ &=x^2-\frac{3}{5}x-(\frac{-2}{5}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-8}{11})(q+\frac{-13}{4})& =(\color{red}{b}+\color{orange}{\frac{-8}{11}}).(\color{green}{q}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{-8}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{4}b-\frac{8}{11}q+\frac{8}{11}.\frac{13}{4}& \text{Uitwerken } \\ & =bq-\frac{13}{4}b-\frac{8}{11}q+\frac{104}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{13}{4}b-\frac{8}{11}q+\frac{26}{11} & \text{Vereenvoudig} \\\end{align}\)
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