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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{4}+b)(\frac{-15}{12}+q)& =(\color{red}{b}+\color{orange}{\frac{-13}{4}}).(\color{green}{q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{4}b-\frac{13}{4}q+\frac{13}{4}.\frac{5}{4}& \text{Uitwerken } \\ & =bq-\frac{5}{4}b-\frac{13}{4}q+\frac{65}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{9}{14}+b)(q+\frac{10}{8})& =(\color{red}{b}+\color{orange}{\frac{9}{14}}).(\color{green}{q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{9}{14})} . \color{green}{(q)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{4}b+\frac{9}{14}q+\frac{9}{14}.\frac{5}{4}& \text{Uitwerken } \\ & =bq+\frac{5}{4}b+\frac{9}{14}q+\frac{45}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{5}{14})(p-\frac{-18}{6})& =(\color{red}{b}+\color{orange}{\frac{5}{14}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(\frac{5}{14})} . \color{green}{(p)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bp+3b+\frac{5}{14}p+\frac{5}{14}.3& \text{Uitwerken } \\ & =bp+3b+\frac{5}{14}p+\frac{15}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-11}{3})(x-\frac{-4}{4})& =(\color{red}{a}+\color{orange}{\frac{11}{3}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{11}{3})} . \color{green}{(x)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1a+\frac{11}{3}x+\frac{11}{3}.1& \text{Uitwerken } \\ & =ax+1a+\frac{11}{3}x+\frac{11}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-7}{12})(a+\frac{-10}{3})& =(\color{red}{q}+\color{orange}{\frac{-7}{12}}).(\color{green}{a}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{10}{3}q-\frac{7}{12}a+\frac{7}{12}.\frac{10}{3}& \text{Uitwerken } \\ & =aq-\frac{10}{3}q-\frac{7}{12}a+\frac{70}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{10}{3}q-\frac{7}{12}a+\frac{35}{18} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-\frac{11}{14})(\frac{6}{11}+b)& =(\color{red}{a}+\color{orange}{\frac{-11}{14}}).(\color{green}{b}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{6}{11}a-\frac{11}{14}b-\frac{11}{14}.\frac{6}{11}& \text{Uitwerken } \\ & =ab+\frac{6}{11}a-\frac{11}{14}b-\frac{66}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{6}{11}a-\frac{11}{14}b-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-15}{19})(x+\frac{-7}{3})& =(\color{red}{b}+\color{orange}{\frac{15}{19}}).(\color{green}{x}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{15}{19})} . \color{green}{(x)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{3}b+\frac{15}{19}x-\frac{15}{19}.\frac{7}{3}& \text{Uitwerken } \\ & =bx-\frac{7}{3}b+\frac{15}{19}x-\frac{105}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{7}{3}b+\frac{15}{19}x-\frac{35}{19} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-20}{12})(\frac{-8}{2}+p)& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = pp-4p+\frac{5}{3}p-\frac{5}{3}.4& \text{Uitwerken } \\ & =p^2+((-4)+\frac{5}{3})p-(\frac{-20}{3}) & \text{Neem samen} \\ &=p^2-\frac{7}{3}p-(\frac{-20}{3}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{16}{3}+b)(b+\frac{16}{15})& =(\color{red}{b}+\color{orange}{\frac{16}{3}}).(\color{green}{b}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{16}{3})} . \color{green}{(b)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{16}{15}b+\frac{16}{3}b+\frac{16}{3}.\frac{16}{15}& \text{Uitwerken } \\ & =b^2+(\frac{16}{15}+\frac{16}{3})b+\frac{256}{45} & \text{Neem samen} \\ &=b^2+\frac{96}{15}b+\frac{256}{45} & \text{Maak de som} \\ &=b^2+\frac{32}{5}b+\frac{256}{45} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(x-\frac{18}{14})(b+(-13))& =(\color{red}{x}+\color{orange}{\frac{-9}{7}}).(\color{green}{b}+\color{blue}{(-13)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-13)} + \color{orange}{(\frac{-9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = bx-13x-\frac{9}{7}b+\frac{9}{7}.13& \text{Uitwerken } \\ & =bx-13x-\frac{9}{7}b+\frac{117}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-4}{17})(\frac{-12}{11}+b)& =(\color{red}{x}+\color{orange}{\frac{4}{17}}).(\color{green}{b}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(\frac{4}{17})} . \color{green}{(b)} + \color{orange}{(\frac{4}{17})} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{12}{11}x+\frac{4}{17}b-\frac{4}{17}.\frac{12}{11}& \text{Uitwerken } \\ & =bx-\frac{12}{11}x+\frac{4}{17}b-\frac{48}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{10}{6})(\frac{-19}{13}-a)& =(\color{red}{a}+\color{orange}{\frac{5}{3}}).(\color{green}{-a}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{19}{13}a-\frac{5}{3}a-\frac{5}{3}.\frac{19}{13}& \text{Uitwerken } \\ & =-a^2+((\frac{-19}{13})+(\frac{-5}{3}))a-\frac{95}{39} & \text{Neem samen} \\ &=-a^2-\frac{122}{39}a-\frac{95}{39} & \text{Maak de som} \\\end{align}\)
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