How can I find the constant term in the expansion (2x-1/x^2)^9? please Thanks alot

1 Answer
Mar 15, 2018

Constant term is #-5376#

Explanation:

#(r+1)^(th)# term in the expansion of #(a+b)^n# is

#C_r^na^(n-r)b^r#

Hence #(r+1)^(th)# term in the expansion of #(2x-1/x^2)^9# is

#C_r^9(2x)^(9-r)(-1/x^2)^r#

= #C_r^9*2^(9-r)*x^(9-r)(-1)^r/x^(2r)#

= #C_r^9*2^(9-r)*x^(9-r-2r)(-1)^r#

= #C_r^9*2^(9-r)(-1)^r*x^(9-3r)#

As we are seeking constant term, this means power of #x# is #0# and hence

#9-3r=0# or #r=3#

and constant term is #C_3^9*2^6(-1)^3#

= #-(9*8*7)/(1*2*3)*64#

= #-84xx64=-5376#