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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{10}{3})(\frac{1}{2}+q)& =(\color{red}{p}+\color{orange}{\frac{10}{3}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{10}{3})} . \color{green}{(q)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{2}p+\frac{10}{3}q+\frac{10}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =pq+\frac{1}{2}p+\frac{10}{3}q+\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{2}p+\frac{10}{3}q+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q-\frac{10}{7})(p-\frac{-11}{18})& =(\color{red}{q}+\color{orange}{\frac{-10}{7}}).(\color{green}{p}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{18}q-\frac{10}{7}p-\frac{10}{7}.\frac{11}{18}& \text{Uitwerken } \\ & =pq+\frac{11}{18}q-\frac{10}{7}p-\frac{110}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{11}{18}q-\frac{10}{7}p-\frac{55}{63} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{15}{9}-b)(\frac{1}{15}+q)& =(\color{red}{-b}+\color{orange}{\frac{5}{3}}).(\color{green}{q}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(\frac{5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{15}b+\frac{5}{3}q+\frac{5}{3}.\frac{1}{15}& \text{Uitwerken } \\ & =-bq-\frac{1}{15}b+\frac{5}{3}q+\frac{5}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{15}b+\frac{5}{3}q+\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a+\frac{5}{18})(\frac{3}{12}-q)& =(\color{red}{a}+\color{orange}{\frac{5}{18}}).(\color{green}{-q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{5}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{4}a-\frac{5}{18}q+\frac{5}{18}.\frac{1}{4}& \text{Uitwerken } \\ & =-aq+\frac{1}{4}a-\frac{5}{18}q+\frac{5}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-12}{9}-a)(\frac{18}{12}-a)& =(\color{red}{-a}+\color{orange}{\frac{-4}{3}}).(\color{green}{-a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{2}a+\frac{4}{3}a-\frac{4}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{2})+\frac{4}{3})a-(\frac{-12}{6}) & \text{Neem samen} \\ &=a^2-\frac{1}{6}a-(\frac{-12}{6}) & \text{Maak de som} \\ &=a^2-\frac{1}{6}a+2 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-10}{17})(b-7)& =(\color{red}{q}+\color{orange}{\frac{-10}{17}}).(\color{green}{b}+\color{blue}{(-7)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-7)} + \color{orange}{(\frac{-10}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = bq-7q-\frac{10}{17}b+\frac{10}{17}.7& \text{Uitwerken } \\ & =bq-7q-\frac{10}{17}b+\frac{70}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+15)(\frac{15}{9}+p)& =(\color{red}{q}+\color{orange}{15}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(15)} . \color{green}{(p)} + \color{orange}{(15)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{3}q+15p+15.\frac{5}{3}& \text{Uitwerken } \\ & =pq+\frac{5}{3}q+15p+\frac{75}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{5}{3}q+15p+25 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-12}{13})(b-\frac{17}{15})& =(\color{red}{b}+\color{orange}{\frac{-12}{13}}).(\color{green}{b}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{17}{15}b-\frac{12}{13}b+\frac{12}{13}.\frac{17}{15}& \text{Uitwerken } \\ & =b^2+((\frac{-17}{15})+(\frac{-12}{13}))b+\frac{204}{195} & \text{Neem samen} \\ &=b^2-\frac{401}{195}b+\frac{204}{195} & \text{Maak de som} \\ &=b^2-\frac{401}{195}b+\frac{68}{65} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-11}{13}+q)(\frac{-16}{6}+a)& =(\color{red}{q}+\color{orange}{\frac{-11}{13}}).(\color{green}{a}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{8}{3}q-\frac{11}{13}a+\frac{11}{13}.\frac{8}{3}& \text{Uitwerken } \\ & =aq-\frac{8}{3}q-\frac{11}{13}a+\frac{88}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-8}{12}+b)(b+\frac{-3}{15})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{5}b-\frac{2}{3}b+\frac{2}{3}.\frac{1}{5}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{5})+(\frac{-2}{3}))b+\frac{2}{15} & \text{Neem samen} \\ &=b^2-\frac{13}{15}b+\frac{2}{15} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a-(-4))(\frac{14}{18}-b)& =(\color{red}{a}+\color{orange}{4}).(\color{green}{-b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(4)} . \color{green}{(-b)} + \color{orange}{(4)} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{7}{9}a-4b+4.\frac{7}{9}& \text{Uitwerken } \\ & =-ab+\frac{7}{9}a-4b+\frac{28}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-17}{19})(x+\frac{-10}{9})& =(\color{red}{q}+\color{orange}{\frac{-17}{19}}).(\color{green}{x}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{10}{9}q-\frac{17}{19}x+\frac{17}{19}.\frac{10}{9}& \text{Uitwerken } \\ & =qx-\frac{10}{9}q-\frac{17}{19}x+\frac{170}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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