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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{3}+x)(x+\frac{15}{19})& =(\color{red}{x}+\color{orange}{\frac{-13}{3}}).(\color{green}{x}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(\frac{-13}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{15}{19}x-\frac{13}{3}x-\frac{13}{3}.\frac{15}{19}& \text{Uitwerken } \\ & =x^2+(\frac{15}{19}+(\frac{-13}{3}))x-(\frac{-195}{57}) & \text{Neem samen} \\ &=x^2-\frac{202}{57}x-(\frac{-195}{57}) & \text{Maak de som} \\ &=x^2-\frac{202}{57}x+\frac{65}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(a-\frac{11}{14})(\frac{13}{7}-a)& =(\color{red}{a}+\color{orange}{\frac{-11}{14}}).(\color{green}{-a}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{13}{7}a+\frac{11}{14}a-\frac{11}{14}.\frac{13}{7}& \text{Uitwerken } \\ & =-a^2+(\frac{13}{7}+\frac{11}{14})a-\frac{143}{98} & \text{Neem samen} \\ &=-a^2+\frac{37}{14}a-\frac{143}{98} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(a+\frac{15}{13})(q-\frac{7}{2})& =(\color{red}{a}+\color{orange}{\frac{15}{13}}).(\color{green}{q}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{15}{13})} . \color{green}{(q)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{2}a+\frac{15}{13}q-\frac{15}{13}.\frac{7}{2}& \text{Uitwerken } \\ & =aq-\frac{7}{2}a+\frac{15}{13}q-\frac{105}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-13}{5}-b)(\frac{18}{6}+a)& =(\color{red}{-b}+\color{orange}{\frac{-13}{5}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(3)} + \color{orange}{(\frac{-13}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{5})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -ab-3b-\frac{13}{5}a-\frac{13}{5}.3& \text{Uitwerken } \\ & =-ab-3b-\frac{13}{5}a-\frac{39}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-11}{5})(2+x)& =(\color{red}{p}+\color{orange}{\frac{11}{5}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{11}{5})} . \color{green}{(x)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = px+2p+\frac{11}{5}x+\frac{11}{5}.2& \text{Uitwerken } \\ & =px+2p+\frac{11}{5}x+\frac{22}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-10}{18}-p)(\frac{-13}{19}+b)& =(\color{red}{-p}+\color{orange}{\frac{-5}{9}}).(\color{green}{b}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{19}p-\frac{5}{9}b+\frac{5}{9}.\frac{13}{19}& \text{Uitwerken } \\ & =-bp+\frac{13}{19}p-\frac{5}{9}b+\frac{65}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{1}{12})(q-\frac{16}{9})& =(\color{red}{q}+\color{orange}{\frac{-1}{12}}).(\color{green}{q}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-1}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{12})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{16}{9}q-\frac{1}{12}q+\frac{1}{12}.\frac{16}{9}& \text{Uitwerken } \\ & =q^2+((\frac{-16}{9})+(\frac{-1}{12}))q+\frac{16}{108} & \text{Neem samen} \\ &=q^2-\frac{67}{36}q+\frac{16}{108} & \text{Maak de som} \\ &=q^2-\frac{67}{36}q+\frac{4}{27} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-1}{2})(a+\frac{1}{17})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{17}x+\frac{1}{2}a+\frac{1}{2}.\frac{1}{17}& \text{Uitwerken } \\ & =ax+\frac{1}{17}x+\frac{1}{2}a+\frac{1}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-8}{15})(b+\frac{3}{3})& =(\color{red}{p}+\color{orange}{\frac{-8}{15}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-8}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p-\frac{8}{15}b-\frac{8}{15}.1& \text{Uitwerken } \\ & =bp+1p-\frac{8}{15}b-\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{8}{17})(x-\frac{4}{2})& =(\color{red}{q}+\color{orange}{\frac{8}{17}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{8}{17})} . \color{green}{(x)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx-2q+\frac{8}{17}x-\frac{8}{17}.2& \text{Uitwerken } \\ & =qx-2q+\frac{8}{17}x-\frac{16}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{6}{3})((-10)+b)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{(-10)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-10)} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = bp-10p-2b+2.10& \text{Uitwerken } \\ & =bp-10p-2b+20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{20}{19})(a-\frac{13}{6})& =(\color{red}{b}+\color{orange}{\frac{20}{19}}).(\color{green}{a}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{20}{19})} . \color{green}{(a)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{6}b+\frac{20}{19}a-\frac{20}{19}.\frac{13}{6}& \text{Uitwerken } \\ & =ab-\frac{13}{6}b+\frac{20}{19}a-\frac{260}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{13}{6}b+\frac{20}{19}a-\frac{130}{57} & \text{Vereenvoudig} \\\end{align}\)
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