Question

The coefficient of a^–6b⁴ in the expansion of `(1/a - (2b)/3)^10` is ______.

Answer 1

The coefficient of a^–6b⁴ in the expansion of `(1/a - (2b)/3)^10` is `1120/27`.

Explanation:

The given expansion is `(1/a - (2b)/3)^10`

From a^–6b⁴ 

We can take r = 4

∴ T₅ = T₄₊₁

= `""^10"C"_4 (1/a)^(10 - 4) (- (2b)/3)^4`

= `""^10"C"_4 (1/a)^6 ((-2)/3)^4 * b^4`

= `(10*9*8*7)/(4*3*2*1) xx 16/81 * a^-6b^4`

= `210 xx 16/81 a^-6b^4`

= `1120/27 a^-6b^4`