Just expand it and you'll get the answer :p

Algebra Level 3

What is the sum of all coefficients in expansion of ( 1 + x − 3 x 2 ) 2017 (1+x-3x^{2})^{2017} ?

Try another one here .

2 2017 2^{2017} 2017 0 -1 − ( 2 2017 + 3 2016 ) -(2^{2017}+3^{2016}) 1

Farhabi Mojib by Farhabi Mojib , 23, Bangladesh

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1 solution

Let f ( x ) = ( 1 + x − 3 x 2 ) 2017 f(x) = \left(1+x-3x^2\right)^{2017} . The sum of all coefficients is given by f ( 1 ) = ( 1 + 1 − 3 ( 1 2 ) ) 2017 = ( − 1 ) 2017 = − 1 f(1) = \left(1+1-3(1^2)\right)^{2017} = (-1)^{2017} = \boxed{-1} .

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