Question

What is the coefficient of the x^5y^5 term in the binomial expansion of (2x-3y)^10?

Answer 1

second one

Explanation:

Answer 2

`10C_5(2)^(5)( - 3)^5`

EXPLANATION

The given binomial expression is

`(2x-3y)^(10)`

The nth term in this expansion is calculated using the formula,

`T_(r+1) = nC_ra^(n-r)b^r`

To find the term with coefficient

`{x}^(5) {y}^(5)`

we substitute r=5, n=10, a=2x, and b=-3y

`T_(6) = 10C_5(2x)^(10-5)( - 3y)^5`

`T_(6) = 10C_5(2x)^(5)( - 3y)^5`

`T_(6) = 10C_5(2)^(5)( - 3)^5 {x}^(5) {y}^(5)`

The coefficient is

`10C_5(2)^(5)( - 3)^5`

The second choice is correct.