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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-12}{11}-p)(q+\frac{-18}{12})& =(\color{red}{-p}+\color{orange}{\frac{-12}{11}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{2}p-\frac{12}{11}q+\frac{12}{11}.\frac{3}{2}& \text{Uitwerken } \\ & =-pq+\frac{3}{2}p-\frac{12}{11}q+\frac{36}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{3}{2}p-\frac{12}{11}q+\frac{18}{11} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-3}{13}+x)(\frac{-4}{13}+p)& =(\color{red}{x}+\color{orange}{\frac{-3}{13}}).(\color{green}{p}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{13}x-\frac{3}{13}p+\frac{3}{13}.\frac{4}{13}& \text{Uitwerken } \\ & =px-\frac{4}{13}x-\frac{3}{13}p+\frac{12}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{17}{14})(b-(-1))& =(\color{red}{b}+\color{orange}{\frac{17}{14}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{17}{14})} . \color{green}{(b)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bb+1b+\frac{17}{14}b+\frac{17}{14}.1& \text{Uitwerken } \\ & =b^2+(1+\frac{17}{14})b+\frac{17}{14} & \text{Neem samen} \\ &=b^2+\frac{31}{14}b+\frac{17}{14} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-10}{14})(\frac{-12}{16}-a)& =(\color{red}{x}+\color{orange}{\frac{-5}{7}}).(\color{green}{-a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{4}x+\frac{5}{7}a+\frac{5}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =-ax-\frac{3}{4}x+\frac{5}{7}a+\frac{15}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-13}{19})((-11)+q)& =(\color{red}{a}+\color{orange}{\frac{13}{19}}).(\color{green}{q}+\color{blue}{(-11)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-11)} + \color{orange}{(\frac{13}{19})} . \color{green}{(q)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = aq-11a+\frac{13}{19}q-\frac{13}{19}.11& \text{Uitwerken } \\ & =aq-11a+\frac{13}{19}q-\frac{143}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-7}{19})(\frac{-17}{10}+b)& =(\color{red}{p}+\color{orange}{\frac{7}{19}}).(\color{green}{b}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{7}{19})} . \color{green}{(b)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{17}{10}p+\frac{7}{19}b-\frac{7}{19}.\frac{17}{10}& \text{Uitwerken } \\ & =bp-\frac{17}{10}p+\frac{7}{19}b-\frac{119}{190} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-16}{3})(b+\frac{-11}{10})& =(\color{red}{b}+\color{orange}{\frac{16}{3}}).(\color{green}{b}+\color{blue}{\frac{-11}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{10})} + \color{orange}{(\frac{16}{3})} . \color{green}{(b)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-11}{10})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{11}{10}b+\frac{16}{3}b-\frac{16}{3}.\frac{11}{10}& \text{Uitwerken } \\ & =b^2+((\frac{-11}{10})+\frac{16}{3})b-(\frac{-176}{30}) & \text{Neem samen} \\ &=b^2+\frac{127}{30}b-(\frac{-176}{30}) & \text{Maak de som} \\ &=b^2+\frac{127}{30}b+\frac{88}{15} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(b+\frac{4}{11})(p+\frac{-19}{17})& =(\color{red}{b}+\color{orange}{\frac{4}{11}}).(\color{green}{p}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{4}{11})} . \color{green}{(p)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{17}b+\frac{4}{11}p-\frac{4}{11}.\frac{19}{17}& \text{Uitwerken } \\ & =bp-\frac{19}{17}b+\frac{4}{11}p-\frac{76}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-1}{4})(p-\frac{19}{7})& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{p}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{7}b+\frac{1}{4}p-\frac{1}{4}.\frac{19}{7}& \text{Uitwerken } \\ & =bp-\frac{19}{7}b+\frac{1}{4}p-\frac{19}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-6}{10})(\frac{19}{17}+q)& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{q}+\color{blue}{\frac{19}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{19}{17})} + \color{orange}{(\frac{3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{19}{17})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{19}{17}q+\frac{3}{5}q+\frac{3}{5}.\frac{19}{17}& \text{Uitwerken } \\ & =q^2+(\frac{19}{17}+\frac{3}{5})q+\frac{57}{85} & \text{Neem samen} \\ &=q^2+\frac{146}{85}q+\frac{57}{85} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}((-3)-x)(\frac{4}{14}+q)& =(\color{red}{-x}+\color{orange}{(-3)}).(\color{green}{q}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(-3)} . \color{green}{(q)} + \color{orange}{(-3)} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{7}x-3q-3.\frac{2}{7}& \text{Uitwerken } \\ & =-qx-\frac{2}{7}x-3q-\frac{6}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-7}{11}+b)(\frac{-19}{17}-b)& =(\color{red}{b}+\color{orange}{\frac{-7}{11}}).(\color{green}{-b}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{19}{17}b+\frac{7}{11}b+\frac{7}{11}.\frac{19}{17}& \text{Uitwerken } \\ & =-b^2+((\frac{-19}{17})+\frac{7}{11})b+(\frac{-133}{187}) & \text{Neem samen} \\ &=-b^2-\frac{90}{187}b+(\frac{-133}{187}) & \text{Maak de som} \\\end{align}\)
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