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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-18}{9}-p)(x-\frac{2}{16})& =(\color{red}{-p}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{8}p-2x+2.\frac{1}{8}& \text{Uitwerken } \\ & =-px+\frac{1}{8}p-2x+\frac{2}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{1}{8}p-2x+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x+\frac{-8}{13})(\frac{-7}{19}-a)& =(\color{red}{x}+\color{orange}{\frac{-8}{13}}).(\color{green}{-a}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{-8}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-8}{13})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{7}{19}x+\frac{8}{13}a+\frac{8}{13}.\frac{7}{19}& \text{Uitwerken } \\ & =-ax-\frac{7}{19}x+\frac{8}{13}a+\frac{56}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{13}{13})(a-\frac{-20}{9})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{20}{9}x+1a+1.\frac{20}{9}& \text{Uitwerken } \\ & =ax+\frac{20}{9}x+1a+\frac{20}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-14}{14})(q-\frac{10}{18})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{9}a-1q+1.\frac{5}{9}& \text{Uitwerken } \\ & =aq-\frac{5}{9}a-1q+\frac{5}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+\frac{4}{16})(\frac{12}{7}-b)& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{-b}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{12}{7}x-\frac{1}{4}b+\frac{1}{4}.\frac{12}{7}& \text{Uitwerken } \\ & =-bx+\frac{12}{7}x-\frac{1}{4}b+\frac{12}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{12}{7}x-\frac{1}{4}b+\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-5}{18})(\frac{-12}{18}+a)& =(\color{red}{a}+\color{orange}{\frac{5}{18}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{5}{18})} . \color{green}{(a)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{2}{3}a+\frac{5}{18}a-\frac{5}{18}.\frac{2}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-2}{3})+\frac{5}{18})a-(\frac{-10}{54}) & \text{Neem samen} \\ &=a^2-\frac{7}{18}a-(\frac{-10}{54}) & \text{Maak de som} \\ &=a^2-\frac{7}{18}a+\frac{5}{27} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(p-\frac{6}{8})(b+\frac{-7}{9})& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{9}p-\frac{3}{4}b+\frac{3}{4}.\frac{7}{9}& \text{Uitwerken } \\ & =bp-\frac{7}{9}p-\frac{3}{4}b+\frac{21}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{7}{9}p-\frac{3}{4}b+\frac{7}{12} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-8}{16})(\frac{-15}{20}+a)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{4}p-\frac{1}{2}a+\frac{1}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =ap-\frac{3}{4}p-\frac{1}{2}a+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+(-4))(a+\frac{-14}{17})& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{14}{17}p-4a+4.\frac{14}{17}& \text{Uitwerken } \\ & =ap-\frac{14}{17}p-4a+\frac{56}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-19}{20}-x)(\frac{15}{3}-q)& =(\color{red}{-x}+\color{orange}{\frac{-19}{20}}).(\color{green}{-q}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(5)} + \color{orange}{(\frac{-19}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = qx-5x+\frac{19}{20}q-\frac{19}{20}.5& \text{Uitwerken } \\ & =qx-5x+\frac{19}{20}q-\frac{95}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-5x+\frac{19}{20}q-\frac{19}{4} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b+\frac{16}{19})(q-\frac{-12}{2})& =(\color{red}{b}+\color{orange}{\frac{16}{19}}).(\color{green}{q}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(6)} + \color{orange}{(\frac{16}{19})} . \color{green}{(q)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bq+6b+\frac{16}{19}q+\frac{16}{19}.6& \text{Uitwerken } \\ & =bq+6b+\frac{16}{19}q+\frac{96}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-18}{20})(\frac{-20}{13}-x)& =(\color{red}{p}+\color{orange}{\frac{9}{10}}).(\color{green}{-x}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{9}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{20}{13}p-\frac{9}{10}x-\frac{9}{10}.\frac{20}{13}& \text{Uitwerken } \\ & =-px-\frac{20}{13}p-\frac{9}{10}x-\frac{180}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{20}{13}p-\frac{9}{10}x-\frac{18}{13} & \text{Vereenvoudig} \\\end{align}\)
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