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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{13}{11}-p)(q+\frac{15}{11})& =(\color{red}{-p}+\color{orange}{\frac{13}{11}}).(\color{green}{q}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{13}{11})} . \color{green}{(q)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{15}{11}p+\frac{13}{11}q+\frac{13}{11}.\frac{15}{11}& \text{Uitwerken } \\ & =-pq-\frac{15}{11}p+\frac{13}{11}q+\frac{195}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{15}{14})(q+\frac{-3}{2})& =(\color{red}{p}+\color{orange}{\frac{-15}{14}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{2}p-\frac{15}{14}q+\frac{15}{14}.\frac{3}{2}& \text{Uitwerken } \\ & =pq-\frac{3}{2}p-\frac{15}{14}q+\frac{45}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{15}{12})(\frac{-4}{11}-x)& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{-x}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{4}{11}a-\frac{5}{4}x-\frac{5}{4}.\frac{4}{11}& \text{Uitwerken } \\ & =-ax-\frac{4}{11}a-\frac{5}{4}x-\frac{20}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{4}{11}a-\frac{5}{4}x-\frac{5}{11} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-1}{3})(p-\frac{9}{10})& =(\color{red}{q}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{9}{10}q+\frac{1}{3}p-\frac{1}{3}.\frac{9}{10}& \text{Uitwerken } \\ & =pq-\frac{9}{10}q+\frac{1}{3}p-\frac{9}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{9}{10}q+\frac{1}{3}p-\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{18}{10}-p)(b+\frac{7}{2})& =(\color{red}{-p}+\color{orange}{\frac{9}{5}}).(\color{green}{b}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{9}{5})} . \color{green}{(b)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{2}p+\frac{9}{5}b+\frac{9}{5}.\frac{7}{2}& \text{Uitwerken } \\ & =-bp-\frac{7}{2}p+\frac{9}{5}b+\frac{63}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{16}{13}+x)(x-\frac{-12}{11})& =(\color{red}{x}+\color{orange}{\frac{16}{13}}).(\color{green}{x}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{16}{13})} . \color{green}{(x)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{12}{11}x+\frac{16}{13}x+\frac{16}{13}.\frac{12}{11}& \text{Uitwerken } \\ & =x^2+(\frac{12}{11}+\frac{16}{13})x+\frac{192}{143} & \text{Neem samen} \\ &=x^2+\frac{332}{143}x+\frac{192}{143} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-10}{8})(\frac{14}{8}-p)& =(\color{red}{p}+\color{orange}{\frac{5}{4}}).(\color{green}{-p}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{7}{4}p-\frac{5}{4}p+\frac{5}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{7}{4}+(\frac{-5}{4}))p+(\frac{-35}{16}) & \text{Neem samen} \\ &=-p^2+\frac{2}{4}p+(\frac{-35}{16}) & \text{Maak de som} \\ &=-p^2+\frac{1}{2}p+(\frac{-35}{16}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{6}{8}-x)(\frac{-20}{3}-b)& =(\color{red}{-x}+\color{orange}{\frac{3}{4}}).(\color{green}{-b}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{20}{3}x-\frac{3}{4}b-\frac{3}{4}.\frac{20}{3}& \text{Uitwerken } \\ & =bx+\frac{20}{3}x-\frac{3}{4}b-\frac{60}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{20}{3}x-\frac{3}{4}b-5 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-3}{8}+x)(a+\frac{2}{13})& =(\color{red}{x}+\color{orange}{\frac{-3}{8}}).(\color{green}{a}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{13}x-\frac{3}{8}a-\frac{3}{8}.\frac{2}{13}& \text{Uitwerken } \\ & =ax+\frac{2}{13}x-\frac{3}{8}a-\frac{6}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{13}x-\frac{3}{8}a-\frac{3}{52} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-20}{9}+b)(12+b)& =(\color{red}{b}+\color{orange}{\frac{-20}{9}}).(\color{green}{b}+\color{blue}{12})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(12)} + \color{orange}{(\frac{-20}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = bb+12b-\frac{20}{9}b-\frac{20}{9}.12& \text{Uitwerken } \\ & =b^2+(12+(\frac{-20}{9}))b-(\frac{-240}{9}) & \text{Neem samen} \\ &=b^2+\frac{88}{9}b-(\frac{-240}{9}) & \text{Maak de som} \\ &=b^2+\frac{88}{9}b+\frac{80}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(\frac{-18}{18}+x)(a-\frac{-2}{4})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}x-1a-1.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}x-1a-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-9}{16})(q-\frac{20}{11})& =(\color{red}{x}+\color{orange}{\frac{9}{16}}).(\color{green}{q}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{9}{16})} . \color{green}{(q)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{20}{11}x+\frac{9}{16}q-\frac{9}{16}.\frac{20}{11}& \text{Uitwerken } \\ & =qx-\frac{20}{11}x+\frac{9}{16}q-\frac{180}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{20}{11}x+\frac{9}{16}q-\frac{45}{44} & \text{Vereenvoudig} \\\end{align}\)
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