Find the coefficient of a5b7 in (a – 2b)12

Asked by Abhisek | 1 year ago |  123

##### Solution :-

The general term Tr+1 in the binomial expansion is given by Tr+1 = 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

Answered by Pragya Singh | 1 year ago

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