Coefficient of a particular power of x
 Let the particular power occur in the (r+1)^{th} term.
 Write the (r+1)^{th} term of the given binomial.
 Equate the power of x in the (r+1)^{th} term and the given power.
 Evaluate r and substitute in in step 2.
Eample: Find the coefficient of x^{15}2)^{10}.
Solution:
 Let x^{15} occur in the (r+1)^{th} term.
 T_{r+1} = ^{10}C_{r}x^{10r} .(x^{2})^{r}.
 ^{10}C_{r}.x^{10r}.x^{2r}.(1)^{r}.
 = (1)^{r}.^{10}C_{r}x^{10+r}
 x^{10+r} = x^{15}
 r = 5
Terms Independent of x
Procedure
 Let (r+1)^{th} term be the term independent of x.
 Put the power of x in this term equal to zero and evaluate it.
Example: Find the term independent of x in the expansion of (3/2x^{2}  1/3x)^{9}.
Solution:
 Let (r+1)^{th} term be independent of x.
 T_{r+1} = ^{9}C_{r}.(3/2x^{2})^{9r}.(1/3x)^{r}
 Putting 183r = 0, we get r = 6.
 The required term is (1)^{6}.^{9}C_{6}. 3^{3}/2^{3} = ^{9}C_{3}.(1/3^{3}.2^{3} = 7/18
Answer: 7/18
Example: Find the greatest coefficient in the expansion of (1+x)^{10}
Solution:
 Let T_{r+1} have the greatest coefficient.
 Then coefficient of T_{r+1} >= the coefficient of T.
 ^{10}C_{r} >= ^{10}C_{r1}
 (10r+1)/r >= 1 or 11 >= 2r, or r <= 51/2
 Hence upto r = 5 the coefficients increase, the greatest of them being r = 5.
 The greatest coefficient = ^{10}C_{5} = 252
Answer : 252
Directions: Answer the following
