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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-6}{2}-a)(b+\frac{13}{20})& =(\color{red}{-a}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{13}{20}a-3b-3.\frac{13}{20}& \text{Uitwerken } \\ & =-ab-\frac{13}{20}a-3b-\frac{39}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-1}{18})(\frac{-8}{14}+x)& =(\color{red}{p}+\color{orange}{\frac{1}{18}}).(\color{green}{x}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{1}{18})} . \color{green}{(x)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{7}p+\frac{1}{18}x-\frac{1}{18}.\frac{4}{7}& \text{Uitwerken } \\ & =px-\frac{4}{7}p+\frac{1}{18}x-\frac{4}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{4}{7}p+\frac{1}{18}x-\frac{2}{63} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{1}{10}+q)(q-\frac{4}{11})& =(\color{red}{q}+\color{orange}{\frac{1}{10}}).(\color{green}{q}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{1}{10})} . \color{green}{(q)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{4}{11}q+\frac{1}{10}q-\frac{1}{10}.\frac{4}{11}& \text{Uitwerken } \\ & =q^2+((\frac{-4}{11})+\frac{1}{10})q-(\frac{-4}{110}) & \text{Neem samen} \\ &=q^2-\frac{29}{110}q-(\frac{-4}{110}) & \text{Maak de som} \\ &=q^2-\frac{29}{110}q+\frac{2}{55} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(a+\frac{17}{14})(\frac{-17}{10}-p)& =(\color{red}{a}+\color{orange}{\frac{17}{14}}).(\color{green}{-p}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{17}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{10}a-\frac{17}{14}p-\frac{17}{14}.\frac{17}{10}& \text{Uitwerken } \\ & =-ap-\frac{17}{10}a-\frac{17}{14}p-\frac{289}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-12}{8})(\frac{9}{10}-b)& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{-b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{10}p-\frac{3}{2}b+\frac{3}{2}.\frac{9}{10}& \text{Uitwerken } \\ & =-bp+\frac{9}{10}p-\frac{3}{2}b+\frac{27}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{20}+q)(a+\frac{1}{4})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{4}q+1a+1.\frac{1}{4}& \text{Uitwerken } \\ & =aq+\frac{1}{4}q+1a+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{13}-p)(\frac{13}{10}+x)& =(\color{red}{-p}+\color{orange}{\frac{11}{13}}).(\color{green}{x}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{11}{13})} . \color{green}{(x)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{13}{10}p+\frac{11}{13}x+\frac{11}{13}.\frac{13}{10}& \text{Uitwerken } \\ & =-px-\frac{13}{10}p+\frac{11}{13}x+\frac{143}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{13}{10}p+\frac{11}{13}x+\frac{11}{10} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}((-14)-a)(\frac{-20}{19}+q)& =(\color{red}{-a}+\color{orange}{(-14)}).(\color{green}{q}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(-14)} . \color{green}{(q)} + \color{orange}{(-14)} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{20}{19}a-14q+14.\frac{20}{19}& \text{Uitwerken } \\ & =-aq+\frac{20}{19}a-14q+\frac{280}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{20}{4})(\frac{-6}{5}-p)& =(\color{red}{p}+\color{orange}{(-5)}).(\color{green}{-p}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(-5)} . \color{green}{(-p)} + \color{orange}{(-5)} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{6}{5}p+5p+5.\frac{6}{5}& \text{Uitwerken } \\ & =-p^2+((\frac{-6}{5})+5)p+(\frac{-30}{5}) & \text{Neem samen} \\ &=-p^2+\frac{19}{5}p+(\frac{-30}{5}) & \text{Maak de som} \\ &=-p^2+\frac{19}{5}p+(-6) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-9}{14}+a)(q+\frac{17}{13})& =(\color{red}{a}+\color{orange}{\frac{-9}{14}}).(\color{green}{q}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{13}a-\frac{9}{14}q-\frac{9}{14}.\frac{17}{13}& \text{Uitwerken } \\ & =aq+\frac{17}{13}a-\frac{9}{14}q-\frac{153}{182} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{7}{19})(\frac{-4}{8}-b)& =(\color{red}{a}+\color{orange}{\frac{7}{19}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{7}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{2}a-\frac{7}{19}b-\frac{7}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =-ab-\frac{1}{2}a-\frac{7}{19}b-\frac{7}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x-\frac{1}{12})(\frac{-3}{14}+x)& =(\color{red}{x}+\color{orange}{\frac{-1}{12}}).(\color{green}{x}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{-1}{12})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{12})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{14}x-\frac{1}{12}x+\frac{1}{12}.\frac{3}{14}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{14})+(\frac{-1}{12}))x+\frac{3}{168} & \text{Neem samen} \\ &=x^2-\frac{25}{84}x+\frac{3}{168} & \text{Maak de som} \\ &=x^2-\frac{25}{84}x+\frac{1}{56} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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