Find the coefficient of

a⁵b⁷ in (a – 2b)¹² .

The general term T_r+1 in the binomial expansion is given by T_r+1 = ⁿC_r a^n-r b^r

Here a =a , b = -2b & n =12

Putting values

T_r+1 = ¹²C_r a^12-r (-2b)^r……….1

To find a⁵

We equate a^12-r =a⁵

r=7

Putting r = 7 in 1

T₈ = ¹²C₇ a⁵ (-2b)⁷

= -101376 a⁵ b⁷

Hence the coefficient of a⁵b⁷= -101376