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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{7}{4}-x)(x-\frac{14}{19})& =(\color{red}{-x}+\color{orange}{\frac{7}{4}}).(\color{green}{x}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{7}{4})} . \color{green}{(x)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{14}{19}x+\frac{7}{4}x-\frac{7}{4}.\frac{14}{19}& \text{Uitwerken } \\ & =-x^2+(\frac{14}{19}+\frac{7}{4})x-\frac{98}{76} & \text{Neem samen} \\ &=-x^2+\frac{189}{76}x-\frac{98}{76} & \text{Maak de som} \\ &=-x^2+\frac{189}{76}x-\frac{49}{38} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(x-20)(p+\frac{-19}{7})& =(\color{red}{x}+\color{orange}{(-20)}).(\color{green}{p}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(-20)} . \color{green}{(p)} + \color{orange}{(-20)} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{7}x-20p+20.\frac{19}{7}& \text{Uitwerken } \\ & =px-\frac{19}{7}x-20p+\frac{380}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{3}{19})(b-\frac{-16}{4})& =(\color{red}{q}+\color{orange}{\frac{-3}{19}}).(\color{green}{b}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(4)} + \color{orange}{(\frac{-3}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bq+4q-\frac{3}{19}b-\frac{3}{19}.4& \text{Uitwerken } \\ & =bq+4q-\frac{3}{19}b-\frac{12}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-17}{19})(\frac{-3}{7}-b)& =(\color{red}{a}+\color{orange}{\frac{17}{19}}).(\color{green}{-b}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{17}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{7}a-\frac{17}{19}b-\frac{17}{19}.\frac{3}{7}& \text{Uitwerken } \\ & =-ab-\frac{3}{7}a-\frac{17}{19}b-\frac{51}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-16}{7})(\frac{16}{2}+q)& =(\color{red}{a}+\color{orange}{\frac{16}{7}}).(\color{green}{q}+\color{blue}{8})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(\frac{16}{7})} . \color{green}{(q)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = aq+8a+\frac{16}{7}q+\frac{16}{7}.8& \text{Uitwerken } \\ & =aq+8a+\frac{16}{7}q+\frac{128}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-14}{6}+p)(\frac{-12}{18}-p)& =(\color{red}{p}+\color{orange}{\frac{-7}{3}}).(\color{green}{-p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{2}{3}p+\frac{7}{3}p+\frac{7}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-p^2+((\frac{-2}{3})+\frac{7}{3})p+(\frac{-14}{9}) & \text{Neem samen} \\ &=-p^2+\frac{5}{3}p+(\frac{-14}{9}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-8}{16}-a)(\frac{7}{12}-q)& =(\color{red}{-a}+\color{orange}{\frac{-1}{2}}).(\color{green}{-q}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{12}a+\frac{1}{2}q-\frac{1}{2}.\frac{7}{12}& \text{Uitwerken } \\ & =aq-\frac{7}{12}a+\frac{1}{2}q-\frac{7}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-15}{18}+b)(\frac{-14}{5}-p)& =(\color{red}{b}+\color{orange}{\frac{-5}{6}}).(\color{green}{-p}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{14}{5}b+\frac{5}{6}p+\frac{5}{6}.\frac{14}{5}& \text{Uitwerken } \\ & =-bp-\frac{14}{5}b+\frac{5}{6}p+\frac{70}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{14}{5}b+\frac{5}{6}p+\frac{7}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q+\frac{1}{20})(b-\frac{-13}{7})& =(\color{red}{q}+\color{orange}{\frac{1}{20}}).(\color{green}{b}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{1}{20})} . \color{green}{(b)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{7}q+\frac{1}{20}b+\frac{1}{20}.\frac{13}{7}& \text{Uitwerken } \\ & =bq+\frac{13}{7}q+\frac{1}{20}b+\frac{13}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{15}{9}-x)(p-\frac{-15}{17})& =(\color{red}{-x}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{15}{17}x+\frac{5}{3}p+\frac{5}{3}.\frac{15}{17}& \text{Uitwerken } \\ & =-px-\frac{15}{17}x+\frac{5}{3}p+\frac{75}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{15}{17}x+\frac{5}{3}p+\frac{25}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-8}{15})(x+\frac{19}{19})& =(\color{red}{a}+\color{orange}{\frac{8}{15}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{8}{15})} . \color{green}{(x)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1a+\frac{8}{15}x+\frac{8}{15}.1& \text{Uitwerken } \\ & =ax+1a+\frac{8}{15}x+\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-2}{14})(\frac{-14}{10}+x)& =(\color{red}{x}+\color{orange}{\frac{-1}{7}}).(\color{green}{x}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{7}{5}x-\frac{1}{7}x+\frac{1}{7}.\frac{7}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-7}{5})+(\frac{-1}{7}))x+\frac{7}{35} & \text{Neem samen} \\ &=x^2-\frac{54}{35}x+\frac{7}{35} & \text{Maak de som} \\ &=x^2-\frac{54}{35}x+\frac{1}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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