Question

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

Answer 1

ANSWER

$10C_5(2)^{5}( - 3)^5$

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.