find the constant term in the expansion of( 5x5+4x4+3x3+2x2+x+1+x-1+x-2+x-3+x-4+x-5 )2

Dear ajinkya

( 5x⁵+4x⁴+3x³+2x²+x+1+x^-1+x^-2+x^-3+x^-4+x^-5 )²

[(5x⁵+4x⁴+3x³+2x²+x)+1+(x^-1+x^-2+x^-3+x^-4+x^-5 )]²

let A =(5x⁵+4x⁴+3x³+2x²+x) 

B  =(x^-1+x^-2+x^-3+x^-4+x^-5 )

so [A+1+B]² = A² +1 +B² +2A+2AB +2B

clearly    A² +B² +2A+2B  will not contain constant term

so constant term   =  1+ 2( constant term in AB)

                                   =1 + 2[1 +2 +3+4+5]

                                    =31

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