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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-10}{6}+b)(b-\frac{8}{17})& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{b}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{8}{17}b-\frac{5}{3}b+\frac{5}{3}.\frac{8}{17}& \text{Uitwerken } \\ & =b^2+((\frac{-8}{17})+(\frac{-5}{3}))b+\frac{40}{51} & \text{Neem samen} \\ &=b^2-\frac{109}{51}b+\frac{40}{51} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}((-18)-b)(a+(-12))& =(\color{red}{-b}+\color{orange}{(-18)}).(\color{green}{a}+\color{blue}{(-12)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(-12)} + \color{orange}{(-18)} . \color{green}{(a)} + \color{orange}{(-18)} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = -ab+12b-18a+18.12& \text{Uitwerken } \\ & =-ab+12b-18a+216 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{14}{6})(\frac{8}{2}+b)& =(\color{red}{p}+\color{orange}{\frac{7}{3}}).(\color{green}{b}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{7}{3})} . \color{green}{(b)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bp+4p+\frac{7}{3}b+\frac{7}{3}.4& \text{Uitwerken } \\ & =bp+4p+\frac{7}{3}b+\frac{28}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-6}{17}+b)(b-\frac{6}{13})& =(\color{red}{b}+\color{orange}{\frac{-6}{17}}).(\color{green}{b}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{-6}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{6}{13}b-\frac{6}{17}b+\frac{6}{17}.\frac{6}{13}& \text{Uitwerken } \\ & =b^2+((\frac{-6}{13})+(\frac{-6}{17}))b+\frac{36}{221} & \text{Neem samen} \\ &=b^2-\frac{180}{221}b+\frac{36}{221} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-5}{3}+x)(\frac{-19}{14}+q)& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{q}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{14}x-\frac{5}{3}q+\frac{5}{3}.\frac{19}{14}& \text{Uitwerken } \\ & =qx-\frac{19}{14}x-\frac{5}{3}q+\frac{95}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-12}{20})(x+\frac{-14}{5})& =(\color{red}{b}+\color{orange}{\frac{3}{5}}).(\color{green}{x}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{14}{5}b+\frac{3}{5}x-\frac{3}{5}.\frac{14}{5}& \text{Uitwerken } \\ & =bx-\frac{14}{5}b+\frac{3}{5}x-\frac{42}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{1}{13}-p)(b-\frac{8}{7})& =(\color{red}{-p}+\color{orange}{\frac{1}{13}}).(\color{green}{b}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{1}{13})} . \color{green}{(b)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{8}{7}p+\frac{1}{13}b-\frac{1}{13}.\frac{8}{7}& \text{Uitwerken } \\ & =-bp+\frac{8}{7}p+\frac{1}{13}b-\frac{8}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-10}{3})(\frac{-12}{4}+p)& =(\color{red}{b}+\color{orange}{\frac{10}{3}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bp-3b+\frac{10}{3}p-\frac{10}{3}.3& \text{Uitwerken } \\ & =bp-3b+\frac{10}{3}p-\frac{30}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-3b+\frac{10}{3}p-10 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{4}-p)(\frac{12}{12}+x)& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -px-1p+1x+1.1& \text{Uitwerken } \\ & =-px-1p+1x+1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{12}{3}+b)(\frac{19}{6}+b)& =(\color{red}{b}+\color{orange}{4}).(\color{green}{b}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(4)} . \color{green}{(b)} + \color{orange}{(4)} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{19}{6}b+4b+4.\frac{19}{6}& \text{Uitwerken } \\ & =b^2+(\frac{19}{6}+4)b+\frac{76}{6} & \text{Neem samen} \\ &=b^2+\frac{43}{6}b+\frac{76}{6} & \text{Maak de som} \\ &=b^2+\frac{43}{6}b+\frac{38}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-6}{13})(a+\frac{6}{8})& =(\color{red}{a}+\color{orange}{\frac{6}{13}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{6}{13})} . \color{green}{(a)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{4}a+\frac{6}{13}a+\frac{6}{13}.\frac{3}{4}& \text{Uitwerken } \\ & =a^2+(\frac{3}{4}+\frac{6}{13})a+\frac{18}{52} & \text{Neem samen} \\ &=a^2+\frac{63}{52}a+\frac{18}{52} & \text{Maak de som} \\ &=a^2+\frac{63}{52}a+\frac{9}{26} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(p-\frac{20}{13})(x+\frac{18}{8})& =(\color{red}{p}+\color{orange}{\frac{-20}{13}}).(\color{green}{x}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{4}p-\frac{20}{13}x-\frac{20}{13}.\frac{9}{4}& \text{Uitwerken } \\ & =px+\frac{9}{4}p-\frac{20}{13}x-\frac{180}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{9}{4}p-\frac{20}{13}x-\frac{45}{13} & \text{Vereenvoudig} \\\end{align}\)
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