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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-12}{19}-q)(\frac{-6}{12}+a)& =(\color{red}{-q}+\color{orange}{\frac{-12}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{2}q-\frac{12}{19}a+\frac{12}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =-aq+\frac{1}{2}q-\frac{12}{19}a+\frac{12}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{1}{2}q-\frac{12}{19}a+\frac{6}{19} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{15}{14}-p)(a+\frac{-20}{2})& =(\color{red}{-p}+\color{orange}{\frac{15}{14}}).(\color{green}{a}+\color{blue}{(-10)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(-10)} + \color{orange}{(\frac{15}{14})} . \color{green}{(a)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -ap+10p+\frac{15}{14}a-\frac{15}{14}.10& \text{Uitwerken } \\ & =-ap+10p+\frac{15}{14}a-\frac{150}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+10p+\frac{15}{14}a-\frac{75}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{12}+q)(\frac{10}{3}-a)& =(\color{red}{q}+\color{orange}{\frac{-4}{3}}).(\color{green}{-a}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{10}{3}q+\frac{4}{3}a-\frac{4}{3}.\frac{10}{3}& \text{Uitwerken } \\ & =-aq+\frac{10}{3}q+\frac{4}{3}a-\frac{40}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{16}{14}-x)(b+\frac{-5}{16})& =(\color{red}{-x}+\color{orange}{\frac{8}{7}}).(\color{green}{b}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{8}{7})} . \color{green}{(b)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{16}x+\frac{8}{7}b-\frac{8}{7}.\frac{5}{16}& \text{Uitwerken } \\ & =-bx+\frac{5}{16}x+\frac{8}{7}b-\frac{40}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{5}{16}x+\frac{8}{7}b-\frac{5}{14} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{20}{12})(\frac{2}{8}-a)& =(\color{red}{a}+\color{orange}{\frac{-5}{3}}).(\color{green}{-a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{4}a+\frac{5}{3}a-\frac{5}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{4}+\frac{5}{3})a-\frac{5}{12} & \text{Neem samen} \\ &=-a^2+\frac{23}{12}a-\frac{5}{12} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{4}+b)(a+\frac{-20}{9})& =(\color{red}{b}+\color{orange}{\frac{-7}{4}}).(\color{green}{a}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{20}{9}b-\frac{7}{4}a+\frac{7}{4}.\frac{20}{9}& \text{Uitwerken } \\ & =ab-\frac{20}{9}b-\frac{7}{4}a+\frac{140}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{20}{9}b-\frac{7}{4}a+\frac{35}{9} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-12}{2})(\frac{-8}{6}+p)& =(\color{red}{b}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{3}b-6p+6.\frac{4}{3}& \text{Uitwerken } \\ & =bp-\frac{4}{3}b-6p+\frac{24}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{4}{3}b-6p+8 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{17}{18}-x)(\frac{-16}{5}+q)& =(\color{red}{-x}+\color{orange}{\frac{17}{18}}).(\color{green}{q}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{17}{18})} . \color{green}{(q)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{16}{5}x+\frac{17}{18}q-\frac{17}{18}.\frac{16}{5}& \text{Uitwerken } \\ & =-qx+\frac{16}{5}x+\frac{17}{18}q-\frac{272}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{16}{5}x+\frac{17}{18}q-\frac{136}{45} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-(-3))(x+\frac{13}{14})& =(\color{red}{x}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{13}{14}x+3x+3.\frac{13}{14}& \text{Uitwerken } \\ & =x^2+(\frac{13}{14}+3)x+\frac{39}{14} & \text{Neem samen} \\ &=x^2+\frac{55}{14}x+\frac{39}{14} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{14}{16}-b)(p+\frac{14}{6})& =(\color{red}{-b}+\color{orange}{\frac{7}{8}}).(\color{green}{p}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{3}b+\frac{7}{8}p+\frac{7}{8}.\frac{7}{3}& \text{Uitwerken } \\ & =-bp-\frac{7}{3}b+\frac{7}{8}p+\frac{49}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{18}{13}+a)(a+\frac{4}{9})& =(\color{red}{a}+\color{orange}{\frac{18}{13}}).(\color{green}{a}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{18}{13})} . \color{green}{(a)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{4}{9}a+\frac{18}{13}a+\frac{18}{13}.\frac{4}{9}& \text{Uitwerken } \\ & =a^2+(\frac{4}{9}+\frac{18}{13})a+\frac{72}{117} & \text{Neem samen} \\ &=a^2+\frac{214}{117}a+\frac{72}{117} & \text{Maak de som} \\ &=a^2+\frac{214}{117}a+\frac{8}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}((-7)-a)(q+\frac{-17}{19})& =(\color{red}{-a}+\color{orange}{(-7)}).(\color{green}{q}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(-7)} . \color{green}{(q)} + \color{orange}{(-7)} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{17}{19}a-7q+7.\frac{17}{19}& \text{Uitwerken } \\ & =-aq+\frac{17}{19}a-7q+\frac{119}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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