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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{13}{19})(\frac{17}{3}-b)& =(\color{red}{b}+\color{orange}{\frac{-13}{19}}).(\color{green}{-b}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{17}{3}b+\frac{13}{19}b-\frac{13}{19}.\frac{17}{3}& \text{Uitwerken } \\ & =-b^2+(\frac{17}{3}+\frac{13}{19})b-\frac{221}{57} & \text{Neem samen} \\ &=-b^2+\frac{362}{57}b-\frac{221}{57} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(x+11)(x-\frac{-18}{15})& =(\color{red}{x}+\color{orange}{11}).(\color{green}{x}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(11)} . \color{green}{(x)} + \color{orange}{(11)} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{6}{5}x+11x+11.\frac{6}{5}& \text{Uitwerken } \\ & =x^2+(\frac{6}{5}+11)x+\frac{66}{5} & \text{Neem samen} \\ &=x^2+\frac{61}{5}x+\frac{66}{5} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-13}{17}-a)(x-\frac{-13}{9})& =(\color{red}{-a}+\color{orange}{\frac{-13}{17}}).(\color{green}{x}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{13}{9}a-\frac{13}{17}x-\frac{13}{17}.\frac{13}{9}& \text{Uitwerken } \\ & =-ax-\frac{13}{9}a-\frac{13}{17}x-\frac{169}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}((-18)-p)(a+\frac{-19}{9})& =(\color{red}{-p}+\color{orange}{(-18)}).(\color{green}{a}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(-18)} . \color{green}{(a)} + \color{orange}{(-18)} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{9}p-18a+18.\frac{19}{9}& \text{Uitwerken } \\ & =-ap+\frac{19}{9}p-18a+\frac{342}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{19}{9}p-18a+38 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{13}-q)(\frac{8}{9}-b)& =(\color{red}{-q}+\color{orange}{\frac{-16}{13}}).(\color{green}{-b}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{9}q+\frac{16}{13}b-\frac{16}{13}.\frac{8}{9}& \text{Uitwerken } \\ & =bq-\frac{8}{9}q+\frac{16}{13}b-\frac{128}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-7}{16})(p-\frac{-20}{13})& =(\color{red}{q}+\color{orange}{\frac{7}{16}}).(\color{green}{p}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{7}{16})} . \color{green}{(p)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{20}{13}q+\frac{7}{16}p+\frac{7}{16}.\frac{20}{13}& \text{Uitwerken } \\ & =pq+\frac{20}{13}q+\frac{7}{16}p+\frac{140}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{20}{13}q+\frac{7}{16}p+\frac{35}{52} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{14}{14}-b)(\frac{-2}{2}-x)& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx+1b-1x-1.1& \text{Uitwerken } \\ & =bx+1b-1x-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{20}{16})(\frac{-14}{2}+b)& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-7)} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = bp-7p-\frac{5}{4}b+\frac{5}{4}.7& \text{Uitwerken } \\ & =bp-7p-\frac{5}{4}b+\frac{35}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-6}{18}-q)(\frac{15}{13}+a)& =(\color{red}{-q}+\color{orange}{\frac{-1}{3}}).(\color{green}{a}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{15}{13}q-\frac{1}{3}a-\frac{1}{3}.\frac{15}{13}& \text{Uitwerken } \\ & =-aq-\frac{15}{13}q-\frac{1}{3}a-\frac{15}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{15}{13}q-\frac{1}{3}a-\frac{5}{13} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{19}{6}+q)(q+\frac{-4}{9})& =(\color{red}{q}+\color{orange}{\frac{19}{6}}).(\color{green}{q}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{19}{6})} . \color{green}{(q)} + \color{orange}{(\frac{19}{6})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{4}{9}q+\frac{19}{6}q-\frac{19}{6}.\frac{4}{9}& \text{Uitwerken } \\ & =q^2+((\frac{-4}{9})+\frac{19}{6})q-(\frac{-76}{54}) & \text{Neem samen} \\ &=q^2+\frac{49}{18}q-(\frac{-76}{54}) & \text{Maak de som} \\ &=q^2+\frac{49}{18}q+\frac{38}{27} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(b-\frac{4}{5})(q+\frac{-4}{11})& =(\color{red}{b}+\color{orange}{\frac{-4}{5}}).(\color{green}{q}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{11}b-\frac{4}{5}q+\frac{4}{5}.\frac{4}{11}& \text{Uitwerken } \\ & =bq-\frac{4}{11}b-\frac{4}{5}q+\frac{16}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-17}{13})(\frac{4}{16}+p)& =(\color{red}{b}+\color{orange}{\frac{-17}{13}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-17}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{4}b-\frac{17}{13}p-\frac{17}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =bp+\frac{1}{4}b-\frac{17}{13}p-\frac{17}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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