How to find constant term of binomial

Question

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.

Cases[([Minus]2 x^4 [Minus] 5/x)^25 // Expand, x_ /; NumericQ[Simplify[x]]] — Daniel Huber, Jan 28, 2022 at 11:58
Also: In[127]:= Residue[1/x*(-2*x^4 - 5/x)^25, {x, 0}] Out[127]= -162139892578125000000 — Daniel Lichtblau, Jan 28, 2022 at 14:07
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. — Daniel Lichtblau, Jan 29, 2022 at 23:00

Roman · Accepted Answer · 2022-01-28 13:16:57Z

17

Coefficient[(-2*x^4 - 5/x)^25, x, 0]
(*    -162139892578125000000    *)

answered Jan 28, 2022 at 13:16

Roman

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$\begingroup$ Superb, thank you!! $\endgroup$
– Orm
Jan 28, 2022 at 21:51
1

$\begingroup$ Note: SeriesCoefficient is a much safer option (e.g., Coefficient[Exp[x],x,0] returns Exp[x] while SeriesCoefficient returns the expected answer). $\endgroup$
– AccidentalFourierTransform
Jan 29, 2022 at 10:47

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a_User_with_No_namE · Accepted Answer · 2022-01-28 18:08:59Z

6

The following, also, works:

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

Output is

-162139892578125000000

answered Jan 28, 2022 at 18:08

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kglr · Accepted Answer · 2022-01-28 14:34:49Z

5

(-2*x^4 - 5/x)^25 // First @* ExpandAll

-162139892578125000000

answered Jan 28, 2022 at 14:34

kglr

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$\begingroup$ Interesting. Simple way of doing it. Thanks! $\endgroup$
– Orm
Jan 28, 2022 at 21:52

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3 Answers 3