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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-16}{19}+q)(q+\frac{1}{5})& =(\color{red}{q}+\color{orange}{\frac{-16}{19}}).(\color{green}{q}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{5}q-\frac{16}{19}q-\frac{16}{19}.\frac{1}{5}& \text{Uitwerken } \\ & =q^2+(\frac{1}{5}+(\frac{-16}{19}))q-(\frac{-16}{95}) & \text{Neem samen} \\ &=q^2-\frac{61}{95}q-(\frac{-16}{95}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-12}{15})(\frac{14}{8}+x)& =(\color{red}{a}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{4}a-\frac{4}{5}x-\frac{4}{5}.\frac{7}{4}& \text{Uitwerken } \\ & =ax+\frac{7}{4}a-\frac{4}{5}x-\frac{28}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{7}{4}a-\frac{4}{5}x-\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-15}{9}+b)((-15)+p)& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{p}+\color{blue}{(-15)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-15)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = bp-15b-\frac{5}{3}p+\frac{5}{3}.15& \text{Uitwerken } \\ & =bp-15b-\frac{5}{3}p+\frac{75}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-15b-\frac{5}{3}p+25 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-18}{3})(\frac{15}{14}-x)& =(\color{red}{x}+\color{orange}{(-6)}).(\color{green}{-x}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(-6)} . \color{green}{(-x)} + \color{orange}{(-6)} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{15}{14}x+6x-6.\frac{15}{14}& \text{Uitwerken } \\ & =-x^2+(\frac{15}{14}+6)x-\frac{90}{14} & \text{Neem samen} \\ &=-x^2+\frac{99}{14}x-\frac{90}{14} & \text{Maak de som} \\ &=-x^2+\frac{99}{14}x-\frac{45}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(b-\frac{15}{3})(\frac{-14}{16}-q)& =(\color{red}{b}+\color{orange}{(-5)}).(\color{green}{-q}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(-5)} . \color{green}{(-q)} + \color{orange}{(-5)} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{8}b+5q+5.\frac{7}{8}& \text{Uitwerken } \\ & =-bq-\frac{7}{8}b+5q+\frac{35}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}((-17)+b)(b+\frac{11}{15})& =(\color{red}{b}+\color{orange}{(-17)}).(\color{green}{b}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(-17)} . \color{green}{(b)} + \color{orange}{(-17)} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{11}{15}b-17b-17.\frac{11}{15}& \text{Uitwerken } \\ & =b^2+(\frac{11}{15}+(-17))b-(\frac{-187}{15}) & \text{Neem samen} \\ &=b^2-\frac{244}{15}b-(\frac{-187}{15}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(a+\frac{2}{2})(\frac{-3}{10}+a)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{10}a+1a-1.\frac{3}{10}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{10})+1)a-(\frac{-3}{10}) & \text{Neem samen} \\ &=a^2+\frac{7}{10}a-(\frac{-3}{10}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{5}{12}-a)(x+\frac{-19}{19})& =(\color{red}{-a}+\color{orange}{\frac{5}{12}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{12})} . \color{green}{(x)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ax+1a+\frac{5}{12}x-\frac{5}{12}.1& \text{Uitwerken } \\ & =-ax+1a+\frac{5}{12}x-\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+\frac{1}{18})(\frac{-19}{16}-p)& =(\color{red}{x}+\color{orange}{\frac{1}{18}}).(\color{green}{-p}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{1}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{16}x-\frac{1}{18}p-\frac{1}{18}.\frac{19}{16}& \text{Uitwerken } \\ & =-px-\frac{19}{16}x-\frac{1}{18}p-\frac{19}{288} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-17}{16})(p+\frac{12}{9})& =(\color{red}{q}+\color{orange}{\frac{-17}{16}}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{3}q-\frac{17}{16}p-\frac{17}{16}.\frac{4}{3}& \text{Uitwerken } \\ & =pq+\frac{4}{3}q-\frac{17}{16}p-\frac{68}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{4}{3}q-\frac{17}{16}p-\frac{17}{12} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-16}{9})(x+\frac{-7}{20})& =(\color{red}{b}+\color{orange}{\frac{-16}{9}}).(\color{green}{x}+\color{blue}{\frac{-7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{20})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{-7}{20})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{20}b-\frac{16}{9}x+\frac{16}{9}.\frac{7}{20}& \text{Uitwerken } \\ & =bx-\frac{7}{20}b-\frac{16}{9}x+\frac{112}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{7}{20}b-\frac{16}{9}x+\frac{28}{45} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x-\frac{14}{13})(x-\frac{-11}{12})& =(\color{red}{x}+\color{orange}{\frac{-14}{13}}).(\color{green}{x}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{11}{12}x-\frac{14}{13}x-\frac{14}{13}.\frac{11}{12}& \text{Uitwerken } \\ & =x^2+(\frac{11}{12}+(\frac{-14}{13}))x-(\frac{-154}{156}) & \text{Neem samen} \\ &=x^2-\frac{25}{156}x-(\frac{-154}{156}) & \text{Maak de som} \\ &=x^2-\frac{25}{156}x+\frac{77}{78} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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