Question

Which expression represents the sixth term in binomial expansion (2a-3b)^10

Answer 1

Therefore the sixth term in the binomial expansion is$=-{10}C_5(2a)^{5} (3b)^5$

Step-by-step explanation:

Given

$(2a -3b)^{10}$

$=^{10}C_0 (2a)^{10} + ^{10}C_1(2a)^9(-3b)+^{10}C_2(2a)^8(-3b)^2+...............+^{10}C_10(-3b)^{10}$

So,

$T_{n+1}= ^{10}C_n(2a)^{(10-n)} (-3b)^n$

$T_6=T_{(5+1)} =^{10}C_5(2a)^{10-5} (-3b)^5$

Therefore the sixth term in the binomial expansion is= ${10}C_5(2a)^{10-5} (-3b)^5$

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