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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-15}{11}+a)(x-\frac{19}{9})& =(\color{red}{a}+\color{orange}{\frac{-15}{11}}).(\color{green}{x}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{9}a-\frac{15}{11}x+\frac{15}{11}.\frac{19}{9}& \text{Uitwerken } \\ & =ax-\frac{19}{9}a-\frac{15}{11}x+\frac{285}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{19}{9}a-\frac{15}{11}x+\frac{95}{33} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q+\frac{3}{18})(a+\frac{2}{18})& =(\color{red}{q}+\color{orange}{\frac{1}{6}}).(\color{green}{a}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{9}q+\frac{1}{6}a+\frac{1}{6}.\frac{1}{9}& \text{Uitwerken } \\ & =aq+\frac{1}{9}q+\frac{1}{6}a+\frac{1}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{14}{16})(q-\frac{14}{5})& =(\color{red}{a}+\color{orange}{\frac{-7}{8}}).(\color{green}{q}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{14}{5}a-\frac{7}{8}q+\frac{7}{8}.\frac{14}{5}& \text{Uitwerken } \\ & =aq-\frac{14}{5}a-\frac{7}{8}q+\frac{98}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{14}{5}a-\frac{7}{8}q+\frac{49}{20} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{17}+b)(\frac{-12}{15}-b)& =(\color{red}{b}+\color{orange}{\frac{9}{17}}).(\color{green}{-b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{9}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{4}{5}b-\frac{9}{17}b-\frac{9}{17}.\frac{4}{5}& \text{Uitwerken } \\ & =-b^2+((\frac{-4}{5})+(\frac{-9}{17}))b-\frac{36}{85} & \text{Neem samen} \\ &=-b^2-\frac{113}{85}b-\frac{36}{85} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}((-14)+q)(p-\frac{16}{14})& =(\color{red}{q}+\color{orange}{(-14)}).(\color{green}{p}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(-14)} . \color{green}{(p)} + \color{orange}{(-14)} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{7}q-14p+14.\frac{8}{7}& \text{Uitwerken } \\ & =pq-\frac{8}{7}q-14p+\frac{112}{7} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{8}{7}q-14p+16 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-10}{3})(p+\frac{12}{14})& =(\color{red}{a}+\color{orange}{\frac{10}{3}}).(\color{green}{p}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{6}{7}a+\frac{10}{3}p+\frac{10}{3}.\frac{6}{7}& \text{Uitwerken } \\ & =ap+\frac{6}{7}a+\frac{10}{3}p+\frac{60}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{6}{7}a+\frac{10}{3}p+\frac{20}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x+\frac{-13}{18})(x+\frac{12}{17})& =(\color{red}{x}+\color{orange}{\frac{-13}{18}}).(\color{green}{x}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{12}{17}x-\frac{13}{18}x-\frac{13}{18}.\frac{12}{17}& \text{Uitwerken } \\ & =x^2+(\frac{12}{17}+(\frac{-13}{18}))x-(\frac{-156}{306}) & \text{Neem samen} \\ &=x^2-\frac{5}{306}x-(\frac{-156}{306}) & \text{Maak de som} \\ &=x^2-\frac{5}{306}x+\frac{26}{51} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(\frac{-7}{16}+b)(\frac{-14}{7}+q)& =(\color{red}{b}+\color{orange}{\frac{-7}{16}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bq-2b-\frac{7}{16}q+\frac{7}{16}.2& \text{Uitwerken } \\ & =bq-2b-\frac{7}{16}q+\frac{14}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-2b-\frac{7}{16}q+\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q+\frac{-20}{18})(\frac{8}{11}-b)& =(\color{red}{q}+\color{orange}{\frac{-10}{9}}).(\color{green}{-b}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{8}{11}q+\frac{10}{9}b-\frac{10}{9}.\frac{8}{11}& \text{Uitwerken } \\ & =-bq+\frac{8}{11}q+\frac{10}{9}b-\frac{80}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}((-7)+a)(q-\frac{-3}{13})& =(\color{red}{a}+\color{orange}{(-7)}).(\color{green}{q}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(-7)} . \color{green}{(q)} + \color{orange}{(-7)} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{13}a-7q-7.\frac{3}{13}& \text{Uitwerken } \\ & =aq+\frac{3}{13}a-7q-\frac{21}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{14}+x)(x-\frac{-6}{16})& =(\color{red}{x}+\color{orange}{\frac{2}{7}}).(\color{green}{x}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{3}{8}x+\frac{2}{7}x+\frac{2}{7}.\frac{3}{8}& \text{Uitwerken } \\ & =x^2+(\frac{3}{8}+\frac{2}{7})x+\frac{6}{56} & \text{Neem samen} \\ &=x^2+\frac{37}{56}x+\frac{6}{56} & \text{Maak de som} \\ &=x^2+\frac{37}{56}x+\frac{3}{28} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(x+\frac{3}{13})(\frac{-16}{15}-b)& =(\color{red}{x}+\color{orange}{\frac{3}{13}}).(\color{green}{-b}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(\frac{3}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{16}{15}x-\frac{3}{13}b-\frac{3}{13}.\frac{16}{15}& \text{Uitwerken } \\ & =-bx-\frac{16}{15}x-\frac{3}{13}b-\frac{48}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{16}{15}x-\frac{3}{13}b-\frac{16}{65} & \text{Vereenvoudig} \\\end{align}\)
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