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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-4}{10}+p)(\frac{8}{9}+b)& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{8}{9}p-\frac{2}{5}b-\frac{2}{5}.\frac{8}{9}& \text{Uitwerken } \\ & =bp+\frac{8}{9}p-\frac{2}{5}b-\frac{16}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{13}{15}-a)((-12)-a)& =(\color{red}{-a}+\color{orange}{\frac{13}{15}}).(\color{green}{-a}+\color{blue}{(-12)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(-12)} + \color{orange}{(\frac{13}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = aa+12a-\frac{13}{15}a-\frac{13}{15}.12& \text{Uitwerken } \\ & =a^2+(12+(\frac{-13}{15}))a-(\frac{-156}{15}) & \text{Neem samen} \\ &=a^2+\frac{167}{15}a-(\frac{-156}{15}) & \text{Maak de som} \\ &=a^2+\frac{167}{15}a+\frac{52}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-3}{10})(p-\frac{-2}{16})& =(\color{red}{p}+\color{orange}{\frac{-3}{10}}).(\color{green}{p}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{8}p-\frac{3}{10}p-\frac{3}{10}.\frac{1}{8}& \text{Uitwerken } \\ & =p^2+(\frac{1}{8}+(\frac{-3}{10}))p-(\frac{-3}{80}) & \text{Neem samen} \\ &=p^2-\frac{7}{40}p-(\frac{-3}{80}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{16}{18}-a)(a+\frac{20}{16})& =(\color{red}{-a}+\color{orange}{\frac{8}{9}}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{5}{4}a+\frac{8}{9}a+\frac{8}{9}.\frac{5}{4}& \text{Uitwerken } \\ & =-a^2+((\frac{-5}{4})+\frac{8}{9})a+(\frac{-40}{36}) & \text{Neem samen} \\ &=-a^2-\frac{13}{36}a+(\frac{-40}{36}) & \text{Maak de som} \\ &=-a^2-\frac{13}{36}a+(\frac{-10}{9}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{17}{4}-p)(b+\frac{18}{12})& =(\color{red}{-p}+\color{orange}{\frac{17}{4}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{17}{4})} . \color{green}{(b)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{2}p+\frac{17}{4}b+\frac{17}{4}.\frac{3}{2}& \text{Uitwerken } \\ & =-bp-\frac{3}{2}p+\frac{17}{4}b+\frac{51}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{12}{4}-x)(\frac{-10}{16}-a)& =(\color{red}{-x}+\color{orange}{3}).(\color{green}{-a}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(3)} . \color{green}{(-a)} + \color{orange}{(3)} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{8}x-3a-3.\frac{5}{8}& \text{Uitwerken } \\ & =ax+\frac{5}{8}x-3a-\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-13}{13})(x+\frac{-19}{5})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{5}q+1x-1.\frac{19}{5}& \text{Uitwerken } \\ & =qx-\frac{19}{5}q+1x-\frac{19}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-1}{9})(\frac{5}{14}+b)& =(\color{red}{a}+\color{orange}{\frac{-1}{9}}).(\color{green}{b}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{14}a-\frac{1}{9}b-\frac{1}{9}.\frac{5}{14}& \text{Uitwerken } \\ & =ab+\frac{5}{14}a-\frac{1}{9}b-\frac{5}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+(-14))(q-\frac{-7}{12})& =(\color{red}{a}+\color{orange}{(-14)}).(\color{green}{q}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(-14)} . \color{green}{(q)} + \color{orange}{(-14)} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{12}a-14q-14.\frac{7}{12}& \text{Uitwerken } \\ & =aq+\frac{7}{12}a-14q-\frac{98}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{7}{12}a-14q-\frac{49}{6} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-10}{20}+a)(a-\frac{14}{12})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{7}{6}a-\frac{1}{2}a+\frac{1}{2}.\frac{7}{6}& \text{Uitwerken } \\ & =a^2+((\frac{-7}{6})+(\frac{-1}{2}))a+\frac{7}{12} & \text{Neem samen} \\ &=a^2-\frac{10}{6}a+\frac{7}{12} & \text{Maak de som} \\ &=a^2-\frac{5}{3}a+\frac{7}{12} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-12}{17})(\frac{-1}{17}+a)& =(\color{red}{b}+\color{orange}{\frac{12}{17}}).(\color{green}{a}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{17}b+\frac{12}{17}a-\frac{12}{17}.\frac{1}{17}& \text{Uitwerken } \\ & =ab-\frac{1}{17}b+\frac{12}{17}a-\frac{12}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-16}{6})(\frac{-19}{10}-b)& =(\color{red}{b}+\color{orange}{\frac{-8}{3}}).(\color{green}{-b}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{19}{10}b+\frac{8}{3}b+\frac{8}{3}.\frac{19}{10}& \text{Uitwerken } \\ & =-b^2+((\frac{-19}{10})+\frac{8}{3})b+(\frac{-152}{30}) & \text{Neem samen} \\ &=-b^2+\frac{23}{30}b+(\frac{-152}{30}) & \text{Maak de som} \\ &=-b^2+\frac{23}{30}b+(\frac{-76}{15}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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