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There is supposed to be a command or set of commands to find the constant term of a binomial expression like

$$ \left(-2x^4 + \dfrac{-5}{x}\right)^{25} $$

(-2*x^4 - 5/x)^25

but I can manage to find it. Help would be greatly appreciated.

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    $\begingroup$ Cases[([Minus]2 x^4 [Minus] 5/x)^25 // Expand, x_ /; NumericQ[Simplify[x]]] $\endgroup$ Jan 28 at 11:58
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    $\begingroup$ Also: In[127]:= Residue[1/x*(-2*x^4 - 5/x)^25, {x, 0}] Out[127]= -162139892578125000000 $\endgroup$ Jan 28 at 14:07
  • $\begingroup$ Moreover (and I make this as a general remark), when you want to find such a term it often pays to look where you last remember having seen it, and retrace your steps from there. $\endgroup$ Jan 29 at 23:00

3 Answers 3

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Coefficient[(-2*x^4 - 5/x)^25, x, 0]
(*    -162139892578125000000    *)
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  • $\begingroup$ Superb, thank you!! $\endgroup$
    – Orm
    Jan 28 at 21:51
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    $\begingroup$ Note: SeriesCoefficient is a much safer option (e.g., Coefficient[Exp[x],x,0] returns Exp[x] while SeriesCoefficient returns the expected answer). $\endgroup$ Jan 29 at 10:47
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The following, also, works:

(-2*x^4 - 5/x)^25 // SeriesCoefficient[#, {x, 0, 0}] &

Output is

-162139892578125000000

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(-2*x^4 - 5/x)^25 // First @* ExpandAll
-162139892578125000000
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  • $\begingroup$ Interesting. Simple way of doing it. Thanks! $\endgroup$
    – Orm
    Jan 28 at 21:52

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