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`

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`