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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{11}{7})(\frac{-9}{10}-q)& =(\color{red}{b}+\color{orange}{\frac{11}{7}}).(\color{green}{-q}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{11}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{10}b-\frac{11}{7}q-\frac{11}{7}.\frac{9}{10}& \text{Uitwerken } \\ & =-bq-\frac{9}{10}b-\frac{11}{7}q-\frac{99}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{4}{14}-b)(b+\frac{13}{2})& =(\color{red}{-b}+\color{orange}{\frac{2}{7}}).(\color{green}{b}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{2}{7})} . \color{green}{(b)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{13}{2}b+\frac{2}{7}b+\frac{2}{7}.\frac{13}{2}& \text{Uitwerken } \\ & =-b^2+((\frac{-13}{2})+\frac{2}{7})b+(\frac{-26}{14}) & \text{Neem samen} \\ &=-b^2-\frac{87}{14}b+(\frac{-26}{14}) & \text{Maak de som} \\ &=-b^2-\frac{87}{14}b+(\frac{-13}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-18}{14})(\frac{-9}{6}-p)& =(\color{red}{q}+\color{orange}{\frac{-9}{7}}).(\color{green}{-p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{2}q+\frac{9}{7}p+\frac{9}{7}.\frac{3}{2}& \text{Uitwerken } \\ & =-pq-\frac{3}{2}q+\frac{9}{7}p+\frac{27}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{7}{3}-q)((-15)+p)& =(\color{red}{-q}+\color{orange}{\frac{7}{3}}).(\color{green}{p}+\color{blue}{(-15)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(-15)} + \color{orange}{(\frac{7}{3})} . \color{green}{(p)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = -pq+15q+\frac{7}{3}p-\frac{7}{3}.15& \text{Uitwerken } \\ & =-pq+15q+\frac{7}{3}p-\frac{105}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+15q+\frac{7}{3}p-35 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{19}-a)(\frac{-14}{10}+a)& =(\color{red}{-a}+\color{orange}{\frac{10}{19}}).(\color{green}{a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{10}{19})} . \color{green}{(a)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{7}{5}a+\frac{10}{19}a-\frac{10}{19}.\frac{7}{5}& \text{Uitwerken } \\ & =-a^2+(\frac{7}{5}+\frac{10}{19})a-\frac{70}{95} & \text{Neem samen} \\ &=-a^2+\frac{183}{95}a-\frac{70}{95} & \text{Maak de som} \\ &=-a^2+\frac{183}{95}a-\frac{14}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(b-\frac{6}{11})(b-\frac{-9}{18})& =(\color{red}{b}+\color{orange}{\frac{-6}{11}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{2}b-\frac{6}{11}b-\frac{6}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =b^2+(\frac{1}{2}+(\frac{-6}{11}))b-(\frac{-6}{22}) & \text{Neem samen} \\ &=b^2-\frac{1}{22}b-(\frac{-6}{22}) & \text{Maak de som} \\ &=b^2-\frac{1}{22}b+\frac{3}{11} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}((-8)+b)(\frac{12}{16}-x)& =(\color{red}{b}+\color{orange}{(-8)}).(\color{green}{-x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(-8)} . \color{green}{(-x)} + \color{orange}{(-8)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{4}b+8x-8.\frac{3}{4}& \text{Uitwerken } \\ & =-bx+\frac{3}{4}b+8x-\frac{24}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{3}{4}b+8x-6 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q-\frac{8}{8})(b+\frac{19}{19})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1q-1b-1.1& \text{Uitwerken } \\ & =bq+1q-1b-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-15}{8}+q)(\frac{2}{14}-b)& =(\color{red}{q}+\color{orange}{\frac{-15}{8}}).(\color{green}{-b}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{7}q+\frac{15}{8}b-\frac{15}{8}.\frac{1}{7}& \text{Uitwerken } \\ & =-bq+\frac{1}{7}q+\frac{15}{8}b-\frac{15}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{16}{18}+q)(\frac{-15}{19}-q)& =(\color{red}{q}+\color{orange}{\frac{8}{9}}).(\color{green}{-q}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{8}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{15}{19}q-\frac{8}{9}q-\frac{8}{9}.\frac{15}{19}& \text{Uitwerken } \\ & =-q^2+((\frac{-15}{19})+(\frac{-8}{9}))q-\frac{120}{171} & \text{Neem samen} \\ &=-q^2-\frac{287}{171}q-\frac{120}{171} & \text{Maak de som} \\ &=-q^2-\frac{287}{171}q-\frac{40}{57} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(a+\frac{-9}{3})(\frac{-6}{14}+a)& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{7}a-3a+3.\frac{3}{7}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{7})+(-3))a+\frac{9}{7} & \text{Neem samen} \\ &=a^2-\frac{24}{7}a+\frac{9}{7} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-19}{12}+b)(\frac{-4}{13}-x)& =(\color{red}{b}+\color{orange}{\frac{-19}{12}}).(\color{green}{-x}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{13}b+\frac{19}{12}x+\frac{19}{12}.\frac{4}{13}& \text{Uitwerken } \\ & =-bx-\frac{4}{13}b+\frac{19}{12}x+\frac{76}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{4}{13}b+\frac{19}{12}x+\frac{19}{39} & \text{Vereenvoudig} \\\end{align}\)
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