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 '22 at 11:58
Also: `In[127]:= Residue[1/x(-2x^4 - 5/x)^25, {x, 0}]
Out[127]= -162139892578125000000` — Daniel Lichtblau, Jan 28 '22 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 '22 at 23:00

score 17 · Answer 1 · answered Jan 28 '22 at 13:16

17

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

answered Jan 28 '22 at 13:16

Roman

Superb, thank you!! – Orm Jan 28 '22 at 21:51
1

Note: SeriesCoefficient is a much safer option (e.g., Coefficient[Exp[x],x,0] returns Exp[x] while SeriesCoefficient returns the expected answer). – AccidentalFourierTransform Jan 29 '22 at 10:47

score 6 · Answer 2 · answered Jan 28 '22 at 18:08

6

The following, also, works:

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

Output is

-162139892578125000000

answered Jan 28 '22 at 18:08

score 5 · Answer 3 · answered Jan 28 '22 at 14:34

5

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

-162139892578125000000

answered Jan 28 '22 at 14:34

kglr

3 Answers3