Question

Find the coefficient of the term x^9 in the expansion of (2x-4)^9 using binomial therorem

Answer 1

Let the rth term contain x^{​​​​9} . In the expansion of (2x - 4)⁹ , rth term is given by

T_r = ⁹C_r-1 . (-1)^r-1 . (2x)^9-r+1 . 4^r-1

      = ⁹​​​​​C_r-1 . (-1)^r-1 . 2^10-r . (2²)^r-1 . x^10-r

     = ⁹C_r-1 . (-1)^r-1 . 2^8-r . x^{​​​​​​10-r}             .... (1)

Since the rth term contains x⁹ , therefore 

10 - r = 9

r = 1 .

From (1), we have

T₁ = ⁹C₀ . (-1)⁰ . 2⁷ . x⁹

      = 128 x⁹

So, coefficient of x⁹ = 128 .

Hence, 128 is the coefficient of x⁹ in the given expansion.