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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{5}{7})(\frac{13}{9}+p)& =(\color{red}{b}+\color{orange}{\frac{5}{7}}).(\color{green}{p}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{5}{7})} . \color{green}{(p)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{9}b+\frac{5}{7}p+\frac{5}{7}.\frac{13}{9}& \text{Uitwerken } \\ & =bp+\frac{13}{9}b+\frac{5}{7}p+\frac{65}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{-17}{19})(\frac{19}{16}-a)& =(\color{red}{x}+\color{orange}{\frac{-17}{19}}).(\color{green}{-a}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{19}{16}x+\frac{17}{19}a-\frac{17}{19}.\frac{19}{16}& \text{Uitwerken } \\ & =-ax+\frac{19}{16}x+\frac{17}{19}a-\frac{323}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{19}{16}x+\frac{17}{19}a-\frac{17}{16} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-2}{14})(q+\frac{7}{20})& =(\color{red}{q}+\color{orange}{\frac{-1}{7}}).(\color{green}{q}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{20}q-\frac{1}{7}q-\frac{1}{7}.\frac{7}{20}& \text{Uitwerken } \\ & =q^2+(\frac{7}{20}+(\frac{-1}{7}))q-(\frac{-7}{140}) & \text{Neem samen} \\ &=q^2+\frac{29}{140}q-(\frac{-7}{140}) & \text{Maak de som} \\ &=q^2+\frac{29}{140}q+\frac{1}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{7}-a)(\frac{4}{9}+b)& =(\color{red}{-a}+\color{orange}{\frac{20}{7}}).(\color{green}{b}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{20}{7})} . \color{green}{(b)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{9}a+\frac{20}{7}b+\frac{20}{7}.\frac{4}{9}& \text{Uitwerken } \\ & =-ab-\frac{4}{9}a+\frac{20}{7}b+\frac{80}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{14}{7})(p+\frac{3}{14})& =(\color{red}{q}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{14}q+2p+2.\frac{3}{14}& \text{Uitwerken } \\ & =pq+\frac{3}{14}q+2p+\frac{6}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{3}{14}q+2p+\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{19}{6}+q)(q+\frac{15}{6})& =(\color{red}{q}+\color{orange}{\frac{19}{6}}).(\color{green}{q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{19}{6})} . \color{green}{(q)} + \color{orange}{(\frac{19}{6})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{5}{2}q+\frac{19}{6}q+\frac{19}{6}.\frac{5}{2}& \text{Uitwerken } \\ & =q^2+(\frac{5}{2}+\frac{19}{6})q+\frac{95}{12} & \text{Neem samen} \\ &=q^2+\frac{34}{6}q+\frac{95}{12} & \text{Maak de som} \\ &=q^2+\frac{17}{3}q+\frac{95}{12} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{19}+x)(x+\frac{-18}{12})& =(\color{red}{x}+\color{orange}{\frac{-14}{19}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{2}x-\frac{14}{19}x+\frac{14}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{2})+(\frac{-14}{19}))x+\frac{42}{38} & \text{Neem samen} \\ &=x^2-\frac{85}{38}x+\frac{42}{38} & \text{Maak de som} \\ &=x^2-\frac{85}{38}x+\frac{21}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}((-18)-a)(p+\frac{-10}{13})& =(\color{red}{-a}+\color{orange}{(-18)}).(\color{green}{p}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(-18)} . \color{green}{(p)} + \color{orange}{(-18)} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{10}{13}a-18p+18.\frac{10}{13}& \text{Uitwerken } \\ & =-ap+\frac{10}{13}a-18p+\frac{180}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+\frac{18}{20})(\frac{5}{6}-q)& =(\color{red}{x}+\color{orange}{\frac{9}{10}}).(\color{green}{-q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{9}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{6}x-\frac{9}{10}q+\frac{9}{10}.\frac{5}{6}& \text{Uitwerken } \\ & =-qx+\frac{5}{6}x-\frac{9}{10}q+\frac{45}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{5}{6}x-\frac{9}{10}q+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a-\frac{3}{4})(\frac{16}{15}-a)& =(\color{red}{a}+\color{orange}{\frac{-3}{4}}).(\color{green}{-a}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{16}{15}a+\frac{3}{4}a-\frac{3}{4}.\frac{16}{15}& \text{Uitwerken } \\ & =-a^2+(\frac{16}{15}+\frac{3}{4})a-\frac{48}{60} & \text{Neem samen} \\ &=-a^2+\frac{109}{60}a-\frac{48}{60} & \text{Maak de som} \\ &=-a^2+\frac{109}{60}a-\frac{4}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-16}{13})(\frac{1}{17}+p)& =(\color{red}{a}+\color{orange}{\frac{16}{13}}).(\color{green}{p}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(\frac{16}{13})} . \color{green}{(p)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{17}a+\frac{16}{13}p+\frac{16}{13}.\frac{1}{17}& \text{Uitwerken } \\ & =ap+\frac{1}{17}a+\frac{16}{13}p+\frac{16}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-\frac{14}{2})(x+\frac{16}{19})& =(\color{red}{q}+\color{orange}{(-7)}).(\color{green}{x}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(-7)} . \color{green}{(x)} + \color{orange}{(-7)} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{16}{19}q-7x-7.\frac{16}{19}& \text{Uitwerken } \\ & =qx+\frac{16}{19}q-7x-\frac{112}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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