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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{18}{2}+b)(p-\frac{17}{15})& =(\color{red}{b}+\color{orange}{9}).(\color{green}{p}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(9)} . \color{green}{(p)} + \color{orange}{(9)} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{17}{15}b+9p-9.\frac{17}{15}& \text{Uitwerken } \\ & =bp-\frac{17}{15}b+9p-\frac{153}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{17}{15}b+9p-\frac{51}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}((-10)-q)(q+\frac{-13}{16})& =(\color{red}{-q}+\color{orange}{(-10)}).(\color{green}{q}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(-10)} . \color{green}{(q)} + \color{orange}{(-10)} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{13}{16}q-10q+10.\frac{13}{16}& \text{Uitwerken } \\ & =-q^2+(\frac{13}{16}+(-10))q+(\frac{-130}{16}) & \text{Neem samen} \\ &=-q^2-\frac{147}{16}q+(\frac{-130}{16}) & \text{Maak de som} \\ &=-q^2-\frac{147}{16}q+(\frac{-65}{8}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-5}{14})(a-\frac{-10}{15})& =(\color{red}{a}+\color{orange}{\frac{5}{14}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{5}{14})} . \color{green}{(a)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{2}{3}a+\frac{5}{14}a+\frac{5}{14}.\frac{2}{3}& \text{Uitwerken } \\ & =a^2+(\frac{2}{3}+\frac{5}{14})a+\frac{10}{42} & \text{Neem samen} \\ &=a^2+\frac{43}{42}a+\frac{10}{42} & \text{Maak de som} \\ &=a^2+\frac{43}{42}a+\frac{5}{21} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{13}{18}-p)(a-\frac{-1}{6})& =(\color{red}{-p}+\color{orange}{\frac{13}{18}}).(\color{green}{a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{13}{18})} . \color{green}{(a)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{6}p+\frac{13}{18}a+\frac{13}{18}.\frac{1}{6}& \text{Uitwerken } \\ & =-ap-\frac{1}{6}p+\frac{13}{18}a+\frac{13}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-19}{18}+x)(a+\frac{8}{8})& =(\color{red}{x}+\color{orange}{\frac{-19}{18}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1x-\frac{19}{18}a-\frac{19}{18}.1& \text{Uitwerken } \\ & =ax+1x-\frac{19}{18}a-\frac{19}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{13}{12})(p+\frac{9}{11})& =(\color{red}{p}+\color{orange}{\frac{-13}{12}}).(\color{green}{p}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{11}p-\frac{13}{12}p-\frac{13}{12}.\frac{9}{11}& \text{Uitwerken } \\ & =p^2+(\frac{9}{11}+(\frac{-13}{12}))p-(\frac{-117}{132}) & \text{Neem samen} \\ &=p^2-\frac{35}{132}p-(\frac{-117}{132}) & \text{Maak de som} \\ &=p^2-\frac{35}{132}p+\frac{39}{44} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{-10}{7}+p)(\frac{-10}{15}+x)& =(\color{red}{p}+\color{orange}{\frac{-10}{7}}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{3}p-\frac{10}{7}x+\frac{10}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =px-\frac{2}{3}p-\frac{10}{7}x+\frac{20}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-19}{14})(b+\frac{10}{9})& =(\color{red}{p}+\color{orange}{\frac{-19}{14}}).(\color{green}{b}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{10}{9}p-\frac{19}{14}b-\frac{19}{14}.\frac{10}{9}& \text{Uitwerken } \\ & =bp+\frac{10}{9}p-\frac{19}{14}b-\frac{190}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{10}{9}p-\frac{19}{14}b-\frac{95}{63} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{17}{14}+x)(p+\frac{16}{20})& =(\color{red}{x}+\color{orange}{\frac{17}{14}}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{17}{14})} . \color{green}{(p)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{4}{5}x+\frac{17}{14}p+\frac{17}{14}.\frac{4}{5}& \text{Uitwerken } \\ & =px+\frac{4}{5}x+\frac{17}{14}p+\frac{68}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{4}{5}x+\frac{17}{14}p+\frac{34}{35} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{10}{20})(b+\frac{9}{4})& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{4}a+\frac{1}{2}b+\frac{1}{2}.\frac{9}{4}& \text{Uitwerken } \\ & =ab+\frac{9}{4}a+\frac{1}{2}b+\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{18}-x)(\frac{4}{19}-q)& =(\color{red}{-x}+\color{orange}{\frac{-19}{18}}).(\color{green}{-q}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{19}x+\frac{19}{18}q-\frac{19}{18}.\frac{4}{19}& \text{Uitwerken } \\ & =qx-\frac{4}{19}x+\frac{19}{18}q-\frac{76}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{4}{19}x+\frac{19}{18}q-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-18}{13})(\frac{13}{10}+a)& =(\color{red}{q}+\color{orange}{\frac{18}{13}}).(\color{green}{a}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{18}{13})} . \color{green}{(a)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{10}q+\frac{18}{13}a+\frac{18}{13}.\frac{13}{10}& \text{Uitwerken } \\ & =aq+\frac{13}{10}q+\frac{18}{13}a+\frac{234}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{13}{10}q+\frac{18}{13}a+\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
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