Q. 23.7( 53 Votes )

# Find the coefficient of

a^{5}b^{7} in (a – 2b)^{12} .

Answer :

The general term T_{r+1} in the binomial expansion is given by T_{r+1} = ^{n}C_{r} a^{n-r} b^{r}

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

Putting values

T_{r+1} = ^{12}C_{r} a^{12-r} (-2b)^{r}……….1

To find a^{5}

We equate a^{12-r} =a^{5}

r=7

Putting r = 7 in 1

T_{8} = ^{12}C_{7} a^{5} (-2b)^{7}

= -101376 a^{5} b^{7}

Hence the coefficient of a^{5}b^{7}= -101376

Rate this question :

Show that the coefficient of x^{4} in the expansion of is .

Show that the middle term in the expansion of is 252.

RS Aggarwal - MathematicsShow that the coefficient of x^{-3} in the expansion of is -330.

Show that the term independent of x in the expansion of is -252.

RS Aggarwal - MathematicsFind the middle term in the expansion of

RS Aggarwal - MathematicsIf the 17^{th} and 18^{th} terms in the expansion of (2 + a)^{50} are equal, find the value of a.