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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{7}{2}+a)(\frac{-16}{2}-q)& =(\color{red}{a}+\color{orange}{\frac{7}{2}}).(\color{green}{-q}+\color{blue}{(-8)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(-8)} + \color{orange}{(\frac{7}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = -aq-8a-\frac{7}{2}q-\frac{7}{2}.8& \text{Uitwerken } \\ & =-aq-8a-\frac{7}{2}q-\frac{56}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-8a-\frac{7}{2}q-28 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{4}+q)(b+\frac{-5}{20})& =(\color{red}{q}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{4}q+2b-2.\frac{1}{4}& \text{Uitwerken } \\ & =bq-\frac{1}{4}q+2b-\frac{2}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{4}q+2b-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-7}{2})(\frac{1}{2}+a)& =(\color{red}{p}+\color{orange}{\frac{7}{2}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{7}{2})} . \color{green}{(a)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{2}p+\frac{7}{2}a+\frac{7}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =ap+\frac{1}{2}p+\frac{7}{2}a+\frac{7}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{13}{11}-a)(p-\frac{7}{8})& =(\color{red}{-a}+\color{orange}{\frac{13}{11}}).(\color{green}{p}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{13}{11})} . \color{green}{(p)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{7}{8}a+\frac{13}{11}p-\frac{13}{11}.\frac{7}{8}& \text{Uitwerken } \\ & =-ap+\frac{7}{8}a+\frac{13}{11}p-\frac{91}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{14}{8})(\frac{-13}{3}+q)& =(\color{red}{p}+\color{orange}{\frac{-7}{4}}).(\color{green}{q}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{3}p-\frac{7}{4}q+\frac{7}{4}.\frac{13}{3}& \text{Uitwerken } \\ & =pq-\frac{13}{3}p-\frac{7}{4}q+\frac{91}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{5}{7}-a)(x+\frac{-20}{17})& =(\color{red}{-a}+\color{orange}{\frac{5}{7}}).(\color{green}{x}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{5}{7})} . \color{green}{(x)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{20}{17}a+\frac{5}{7}x-\frac{5}{7}.\frac{20}{17}& \text{Uitwerken } \\ & =-ax+\frac{20}{17}a+\frac{5}{7}x-\frac{100}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{10}-q)(q-\frac{11}{13})& =(\color{red}{-q}+\color{orange}{\frac{13}{10}}).(\color{green}{q}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{11}{13}q+\frac{13}{10}q-\frac{13}{10}.\frac{11}{13}& \text{Uitwerken } \\ & =-q^2+(\frac{11}{13}+\frac{13}{10})q-\frac{143}{130} & \text{Neem samen} \\ &=-q^2+\frac{279}{130}q-\frac{143}{130} & \text{Maak de som} \\ &=-q^2+\frac{279}{130}q-\frac{11}{10} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-9}{4})(x-\frac{17}{4})& =(\color{red}{x}+\color{orange}{\frac{9}{4}}).(\color{green}{x}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{9}{4})} . \color{green}{(x)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{17}{4}x+\frac{9}{4}x-\frac{9}{4}.\frac{17}{4}& \text{Uitwerken } \\ & =x^2+((\frac{-17}{4})+\frac{9}{4})x-(\frac{-153}{16}) & \text{Neem samen} \\ &=x^2-\frac{8}{4}x-(\frac{-153}{16}) & \text{Maak de som} \\ &=x^2-2x+\frac{153}{16} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(b+\frac{3}{16})(\frac{4}{15}-b)& =(\color{red}{b}+\color{orange}{\frac{3}{16}}).(\color{green}{-b}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{3}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{4}{15}b-\frac{3}{16}b+\frac{3}{16}.\frac{4}{15}& \text{Uitwerken } \\ & =-b^2+(\frac{4}{15}+(\frac{-3}{16}))b+(\frac{-12}{240}) & \text{Neem samen} \\ &=-b^2+\frac{19}{240}b+(\frac{-12}{240}) & \text{Maak de som} \\ &=-b^2+\frac{19}{240}b+(\frac{-1}{20}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(x+\frac{2}{19})(\frac{-2}{18}-q)& =(\color{red}{x}+\color{orange}{\frac{2}{19}}).(\color{green}{-q}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{2}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{9}x-\frac{2}{19}q-\frac{2}{19}.\frac{1}{9}& \text{Uitwerken } \\ & =-qx-\frac{1}{9}x-\frac{2}{19}q-\frac{2}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{-17}{19})(p+\frac{15}{20})& =(\color{red}{a}+\color{orange}{\frac{-17}{19}}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{4}a-\frac{17}{19}p-\frac{17}{19}.\frac{3}{4}& \text{Uitwerken } \\ & =ap+\frac{3}{4}a-\frac{17}{19}p-\frac{51}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-5}{20}+a)(\frac{13}{13}-p)& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1a+\frac{1}{4}p-\frac{1}{4}.1& \text{Uitwerken } \\ & =-ap+1a+\frac{1}{4}p-\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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