Find the 4 th term in the expansion of ( x – 2 y ) 12 .
Given expression ( x − 2 y ) 12 we have to find the value of 4 t h term means value of r is given,
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 ) t h 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 y ) 12 and ( a + b ) n , value of a = x , b = − 2 y and n = 12 .
Thus the general term in the expansion of ( x − 2 y ) 12 is
T 3+1 = C 12 3 ( x ) 12 − 3 ( − 2 y ) 3 = ( − 1 ) 3 C 12 3 x 9 y 3 ( 2 ) 3 = − 12 × 11 × 10 3 × 2 ( 2 ) 3 x 9 y 3 = − 1760 x 9 y 3
Given expression
The formula for binomial expansion is ,
It is known that
General terms expressed as
On comparing both the expression
Thus the general term in the expansion of
