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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{8}{13}+p)(q-\frac{-20}{5})& =(\color{red}{p}+\color{orange}{\frac{8}{13}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{8}{13})} . \color{green}{(q)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = pq+4p+\frac{8}{13}q+\frac{8}{13}.4& \text{Uitwerken } \\ & =pq+4p+\frac{8}{13}q+\frac{32}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{13}{16}+a)(\frac{-19}{4}-p)& =(\color{red}{a}+\color{orange}{\frac{13}{16}}).(\color{green}{-p}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{13}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{19}{4}a-\frac{13}{16}p-\frac{13}{16}.\frac{19}{4}& \text{Uitwerken } \\ & =-ap-\frac{19}{4}a-\frac{13}{16}p-\frac{247}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-11}{7})(p-\frac{-1}{19})& =(\color{red}{x}+\color{orange}{\frac{11}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{11}{7})} . \color{green}{(p)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{19}x+\frac{11}{7}p+\frac{11}{7}.\frac{1}{19}& \text{Uitwerken } \\ & =px+\frac{1}{19}x+\frac{11}{7}p+\frac{11}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-3}{9}+b)(12-q)& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{-q}+\color{blue}{12})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(12)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = -bq+12b+\frac{1}{3}q-\frac{1}{3}.12& \text{Uitwerken } \\ & =-bq+12b+\frac{1}{3}q-\frac{12}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+12b+\frac{1}{3}q-4 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x-\frac{7}{5})(p+\frac{-15}{18})& =(\color{red}{x}+\color{orange}{\frac{-7}{5}}).(\color{green}{p}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{6}x-\frac{7}{5}p+\frac{7}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =px-\frac{5}{6}x-\frac{7}{5}p+\frac{35}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{5}{6}x-\frac{7}{5}p+\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-11}{11})(\frac{-19}{5}-p)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{19}{5}b+1p+1.\frac{19}{5}& \text{Uitwerken } \\ & =-bp-\frac{19}{5}b+1p+\frac{19}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+\frac{12}{9})(\frac{4}{17}+a)& =(\color{red}{b}+\color{orange}{\frac{4}{3}}).(\color{green}{a}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{4}{17}b+\frac{4}{3}a+\frac{4}{3}.\frac{4}{17}& \text{Uitwerken } \\ & =ab+\frac{4}{17}b+\frac{4}{3}a+\frac{16}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{20}{6})(\frac{-12}{15}-a)& =(\color{red}{b}+\color{orange}{\frac{-10}{3}}).(\color{green}{-a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{5}b+\frac{10}{3}a+\frac{10}{3}.\frac{4}{5}& \text{Uitwerken } \\ & =-ab-\frac{4}{5}b+\frac{10}{3}a+\frac{40}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{4}{5}b+\frac{10}{3}a+\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{1}{11})(p+\frac{12}{2})& =(\color{red}{b}+\color{orange}{\frac{-1}{11}}).(\color{green}{p}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(6)} + \color{orange}{(\frac{-1}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bp+6b-\frac{1}{11}p-\frac{1}{11}.6& \text{Uitwerken } \\ & =bp+6b-\frac{1}{11}p-\frac{6}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-14}{9})(p+\frac{-11}{12})& =(\color{red}{q}+\color{orange}{\frac{-14}{9}}).(\color{green}{p}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{12}q-\frac{14}{9}p+\frac{14}{9}.\frac{11}{12}& \text{Uitwerken } \\ & =pq-\frac{11}{12}q-\frac{14}{9}p+\frac{154}{108} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{11}{12}q-\frac{14}{9}p+\frac{77}{54} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{1}{14}-a)(\frac{-15}{3}+a)& =(\color{red}{-a}+\color{orange}{\frac{1}{14}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(-5)} + \color{orange}{(\frac{1}{14})} . \color{green}{(a)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -aa+5a+\frac{1}{14}a-\frac{1}{14}.5& \text{Uitwerken } \\ & =-a^2+(5+\frac{1}{14})a-\frac{5}{14} & \text{Neem samen} \\ &=-a^2+\frac{71}{14}a-\frac{5}{14} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(b+\frac{20}{6})(\frac{-19}{14}-b)& =(\color{red}{b}+\color{orange}{\frac{10}{3}}).(\color{green}{-b}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{10}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{19}{14}b-\frac{10}{3}b-\frac{10}{3}.\frac{19}{14}& \text{Uitwerken } \\ & =-b^2+((\frac{-19}{14})+(\frac{-10}{3}))b-\frac{190}{42} & \text{Neem samen} \\ &=-b^2-\frac{197}{42}b-\frac{190}{42} & \text{Maak de som} \\ &=-b^2-\frac{197}{42}b-\frac{95}{21} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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