What is the coefficient of the x5y5-term in the binomial expansion of (2x – 3y)10? 10C5(2)5(3)5 10C5(2)5(–3)5 –10C5(2)5(–3)5 10C5(2)5(3)

ANSWER[tex]10C_5(2)^{5}( - 3)^5 [/tex]EXPLANATIONThe given binomial expansion is:[tex] {(2x - 3y)}^{10} [/tex]Compare this to [tex] {(a + b)}^{n} [/tex]we have a=2x , b=-3y and n=10We want to find the coefficient of the term[tex] {x}^{5} {y}^{5} [/tex]This implies that, r=5.The terms in the expansion can be obtained using [tex]T_{r+1}=nC_ra^{n-r}b^r[/tex]We substitute the given values to obtain;[tex]T_{5+1}=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]Hence the coefficient is;[tex]10C_5(2)^{5}( - 3)^5 [/tex]