The general term Tr+1 in the binomial expansion is given by Tr+1 = n C r an-r br
Here a = a, b = -2b & n =12
Substituting the values, we get
Tr+1 = 12Cr a12-r (-2b)r………. (i)
To find a5
We equate a12-r =a5
r = 7
Putting r = 7 in (i)
T8 = 12C7 a5 (-2b)7
\( T_8=\dfrac{12!}{7!5!}\times a^5\times (-2)^7b^7\)
= -101376 a5 b7
Hence the coefficient of a5b7= -101376
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