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

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

Grade:10

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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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Badiuddin

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