Question

4. (x2— yx)12, x 01

Answer 1

Given expression ( x 2 −yx ) 12 where x≠0 ask for writing general term.

The formula for binomial expansion is ,

( a+b ) n = C n 0 a n + C n 1 a n−1 b+ C n 2 a n−2 b 2 +..........+ C n n−1 a. b n−1 + C n n b n

It is known that ( r+1 ) th term in T r+1 in binomial expansion of ( a+b ) n ,

General terms expressed as

T r+1 = C n r a n−r ( b ) r

On comparing both the expression ( x 2 −yx ) 12 and ( a+b ) n , value of a= x 2 , b=−yx and n=12 .

Thus the general term in the expansion of ( x 2 −yx ) 12 is

T r+1 = C 12 r ( x 2 ) 12−r ( −yx ) r = ( −1 ) r C 12 r x 24−2r y r x r = ( −1 ) r C 12 r x 24−r y r