Find the coefficient ofa5b7 in (a – 2b)12 .

The general term Tr+1 in the binomial expansion is given by Tr+1 = nCr an-r br

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

Putting values

Tr+1 = 12Cr a12-r (-2b)r……….1

To find a5

We equate a12-r =a5

r=7

Putting r = 7 in 1

T8 = 12C7 a5 (-2b)7

= -101376 a5 b7

Hence the coefficient of a5b7= -101376

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