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

Accepted Solution

ANSWER[tex] 10C_5(2)^{5}( - 3)^5[/tex]EXPLANATIONThe given binomial expression is[tex](2x-3y)^{10} [/tex]The nth term in this expansion is calculated using the formula,[tex]T_{r+1} = nC_ra^{n-r}b^r[/tex]To find the term with coefficient [tex] {x}^{5} {y}^{5} [/tex]we substitute r=5, n=10, a=2x, and b=-3y[tex]T_{6} = 10C_5(2x)^{10-5}( - 3y)^5[/tex][tex]T_{6} = 10C_5(2x)^{5}( - 3y)^5[/tex][tex]T_{6} = 10C_5(2)^{5}( - 3)^5 {x}^{5} {y}^{5} [/tex]The coefficient is[tex] 10C_5(2)^{5}( - 3)^5[/tex]The second choice is correct.