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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{8}{18}+p)(\frac{-3}{12}+q)& =(\color{red}{p}+\color{orange}{\frac{4}{9}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{4}{9})} . \color{green}{(q)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{4}p+\frac{4}{9}q-\frac{4}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =pq-\frac{1}{4}p+\frac{4}{9}q-\frac{4}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{1}{4}p+\frac{4}{9}q-\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{7}{18}-q)(\frac{-15}{12}+b)& =(\color{red}{-q}+\color{orange}{\frac{7}{18}}).(\color{green}{b}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{7}{18})} . \color{green}{(b)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{4}q+\frac{7}{18}b-\frac{7}{18}.\frac{5}{4}& \text{Uitwerken } \\ & =-bq+\frac{5}{4}q+\frac{7}{18}b-\frac{35}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-18}{5}+p)(\frac{-12}{9}+p)& =(\color{red}{p}+\color{orange}{\frac{-18}{5}}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{4}{3}p-\frac{18}{5}p+\frac{18}{5}.\frac{4}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-4}{3})+(\frac{-18}{5}))p+\frac{72}{15} & \text{Neem samen} \\ &=p^2-\frac{74}{15}p+\frac{72}{15} & \text{Maak de som} \\ &=p^2-\frac{74}{15}p+\frac{24}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{-10}{9}-b)(\frac{10}{10}+q)& =(\color{red}{-b}+\color{orange}{\frac{-10}{9}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{-10}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bq-1b-\frac{10}{9}q-\frac{10}{9}.1& \text{Uitwerken } \\ & =-bq-1b-\frac{10}{9}q-\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{11}{12})(b-\frac{-5}{13})& =(\color{red}{b}+\color{orange}{\frac{-11}{12}}).(\color{green}{b}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{13}b-\frac{11}{12}b-\frac{11}{12}.\frac{5}{13}& \text{Uitwerken } \\ & =b^2+(\frac{5}{13}+(\frac{-11}{12}))b-(\frac{-55}{156}) & \text{Neem samen} \\ &=b^2-\frac{83}{156}b-(\frac{-55}{156}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{2}{19}+p)(q-\frac{10}{7})& =(\color{red}{p}+\color{orange}{\frac{2}{19}}).(\color{green}{q}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{2}{19})} . \color{green}{(q)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{10}{7}p+\frac{2}{19}q-\frac{2}{19}.\frac{10}{7}& \text{Uitwerken } \\ & =pq-\frac{10}{7}p+\frac{2}{19}q-\frac{20}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{5}{11})(p-\frac{20}{12})& =(\color{red}{b}+\color{orange}{\frac{-5}{11}}).(\color{green}{p}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{3}b-\frac{5}{11}p+\frac{5}{11}.\frac{5}{3}& \text{Uitwerken } \\ & =bp-\frac{5}{3}b-\frac{5}{11}p+\frac{25}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-15}{17}+q)(q-\frac{-12}{5})& =(\color{red}{q}+\color{orange}{\frac{-15}{17}}).(\color{green}{q}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{-15}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{12}{5}q-\frac{15}{17}q-\frac{15}{17}.\frac{12}{5}& \text{Uitwerken } \\ & =q^2+(\frac{12}{5}+(\frac{-15}{17}))q-(\frac{-180}{85}) & \text{Neem samen} \\ &=q^2+\frac{129}{85}q-(\frac{-180}{85}) & \text{Maak de som} \\ &=q^2+\frac{129}{85}q+\frac{36}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(b-\frac{12}{15})(\frac{11}{11}+x)& =(\color{red}{b}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1b-\frac{4}{5}x-\frac{4}{5}.1& \text{Uitwerken } \\ & =bx+1b-\frac{4}{5}x-\frac{4}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-10}{3}+b)(a+\frac{-11}{12})& =(\color{red}{b}+\color{orange}{\frac{-10}{3}}).(\color{green}{a}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{12}b-\frac{10}{3}a+\frac{10}{3}.\frac{11}{12}& \text{Uitwerken } \\ & =ab-\frac{11}{12}b-\frac{10}{3}a+\frac{110}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{11}{12}b-\frac{10}{3}a+\frac{55}{18} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{10}+q)(\frac{-9}{14}-q)& =(\color{red}{q}+\color{orange}{\frac{7}{5}}).(\color{green}{-q}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{7}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{9}{14}q-\frac{7}{5}q-\frac{7}{5}.\frac{9}{14}& \text{Uitwerken } \\ & =-q^2+((\frac{-9}{14})+(\frac{-7}{5}))q-\frac{63}{70} & \text{Neem samen} \\ &=-q^2-\frac{143}{70}q-\frac{63}{70} & \text{Maak de som} \\ &=-q^2-\frac{143}{70}q-\frac{9}{10} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(p-\frac{12}{9})(q-\frac{18}{3})& =(\color{red}{p}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-6)} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = pq-6p-\frac{4}{3}q+\frac{4}{3}.6& \text{Uitwerken } \\ & =pq-6p-\frac{4}{3}q+\frac{24}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-6p-\frac{4}{3}q+8 & \text{Vereenvoudig} \\\end{align}\)
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