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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-17}{16}-q)(\frac{-18}{19}+a)& =(\color{red}{-q}+\color{orange}{\frac{-17}{16}}).(\color{green}{a}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{18}{19}q-\frac{17}{16}a+\frac{17}{16}.\frac{18}{19}& \text{Uitwerken } \\ & =-aq+\frac{18}{19}q-\frac{17}{16}a+\frac{306}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{18}{19}q-\frac{17}{16}a+\frac{153}{152} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{5}{8}+a)(\frac{-10}{7}+p)& =(\color{red}{a}+\color{orange}{\frac{5}{8}}).(\color{green}{p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{5}{8})} . \color{green}{(p)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{10}{7}a+\frac{5}{8}p-\frac{5}{8}.\frac{10}{7}& \text{Uitwerken } \\ & =ap-\frac{10}{7}a+\frac{5}{8}p-\frac{50}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{10}{7}a+\frac{5}{8}p-\frac{25}{28} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{19}{4}+b)(x-\frac{-16}{17})& =(\color{red}{b}+\color{orange}{\frac{19}{4}}).(\color{green}{x}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{19}{4})} . \color{green}{(x)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{16}{17}b+\frac{19}{4}x+\frac{19}{4}.\frac{16}{17}& \text{Uitwerken } \\ & =bx+\frac{16}{17}b+\frac{19}{4}x+\frac{304}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{16}{17}b+\frac{19}{4}x+\frac{76}{17} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{8}{3})(\frac{1}{4}-b)& =(\color{red}{p}+\color{orange}{\frac{-8}{3}}).(\color{green}{-b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{4}p+\frac{8}{3}b-\frac{8}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =-bp+\frac{1}{4}p+\frac{8}{3}b-\frac{8}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{1}{4}p+\frac{8}{3}b-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x+\frac{1}{6})(\frac{15}{14}+a)& =(\color{red}{x}+\color{orange}{\frac{1}{6}}).(\color{green}{a}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{15}{14}x+\frac{1}{6}a+\frac{1}{6}.\frac{15}{14}& \text{Uitwerken } \\ & =ax+\frac{15}{14}x+\frac{1}{6}a+\frac{15}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{15}{14}x+\frac{1}{6}a+\frac{5}{28} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{17}{13}-q)(\frac{13}{3}-q)& =(\color{red}{-q}+\color{orange}{\frac{17}{13}}).(\color{green}{-q}+\color{blue}{\frac{13}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{3})} + \color{orange}{(\frac{17}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{13}{3})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{13}{3}q-\frac{17}{13}q+\frac{17}{13}.\frac{13}{3}& \text{Uitwerken } \\ & =q^2+((\frac{-13}{3})+(\frac{-17}{13}))q+\frac{221}{39} & \text{Neem samen} \\ &=q^2-\frac{220}{39}q+\frac{221}{39} & \text{Maak de som} \\ &=q^2-\frac{220}{39}q+\frac{17}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{1}{2}-a)(\frac{-19}{4}-p)& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{-p}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{4}a-\frac{1}{2}p-\frac{1}{2}.\frac{19}{4}& \text{Uitwerken } \\ & =ap+\frac{19}{4}a-\frac{1}{2}p-\frac{19}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-16}{18})(q+\frac{17}{13})& =(\color{red}{a}+\color{orange}{\frac{8}{9}}).(\color{green}{q}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{8}{9})} . \color{green}{(q)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{13}a+\frac{8}{9}q+\frac{8}{9}.\frac{17}{13}& \text{Uitwerken } \\ & =aq+\frac{17}{13}a+\frac{8}{9}q+\frac{136}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{16}{17}+q)(\frac{5}{17}+x)& =(\color{red}{q}+\color{orange}{\frac{16}{17}}).(\color{green}{x}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{16}{17})} . \color{green}{(x)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{17}q+\frac{16}{17}x+\frac{16}{17}.\frac{5}{17}& \text{Uitwerken } \\ & =qx+\frac{5}{17}q+\frac{16}{17}x+\frac{80}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-13}{10})(p-(-18))& =(\color{red}{a}+\color{orange}{\frac{13}{10}}).(\color{green}{p}+\color{blue}{18})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(18)} + \color{orange}{(\frac{13}{10})} . \color{green}{(p)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = ap+18a+\frac{13}{10}p+\frac{13}{10}.18& \text{Uitwerken } \\ & =ap+18a+\frac{13}{10}p+\frac{234}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+18a+\frac{13}{10}p+\frac{117}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{9}+b)(a-(-16))& =(\color{red}{b}+\color{orange}{\frac{-19}{9}}).(\color{green}{a}+\color{blue}{16})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(16)} + \color{orange}{(\frac{-19}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = ab+16b-\frac{19}{9}a-\frac{19}{9}.16& \text{Uitwerken } \\ & =ab+16b-\frac{19}{9}a-\frac{304}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-16}{4})(\frac{8}{3}-b)& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{-b}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(-4)} . \color{green}{(-b)} + \color{orange}{(-4)} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{8}{3}x+4b-4.\frac{8}{3}& \text{Uitwerken } \\ & =-bx+\frac{8}{3}x+4b-\frac{32}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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