What is the sum of the coefficients?

Algebra Level pending

Determine the value of the sum of the coefficients in the expansion of

g ( x ) = ( x + 2 ) 3 ( x 2 + 2 x + 1 ) 4 g(x)={ (x+2) }^{ 3 }{ ({ x }^{ 2 }+2x+1) }^{ 4 }


The answer is 6912.

Geoff Taylor by geoff taylor , 71, Canada

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1 solution

Geoff Taylor
Dec 24, 2017

The sum of the coefficients can be determined by letting x = 1 This gives g ( 1 ) = ( 1 + 2 ) 3 ( 1 2 + 2 × 1 + 1 ) 4 = 6912 g(1)={ (1+2) }^{ 3 }{ ({ 1 }^{ 2 }+2\times 1+1) }^{ 4 }=6912

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