T4 = 12 C3( x) 9(-2y) 3
Or T4 =-1760 x 9 y 3 Middle term in the expansion of( a + b) n Case 1:“ n” is even, Total term is expansion: n + 1 à Odd Middle term =( n / 2 + 1) th
We Can now find the middle term using the general term formula, Tr + 1 = n Cr a n – r b r
Case 2:“ n” is odd, total term in expansion: n + 1 à Even There will be two Middle terms =(( n + 1)/ 2) th
&(( n + 1)/ 2 + 1) th terms
We can now find the middle term using the general term formula
Tr + 1 = n Cr a n – r b r
Numerical: Find the middle terms in the expansions of( x / 3 + 9y) 10 Solution: in this case, a = x / 3, b = 9y & n = 10 Since n = 10, number of terms in the expansion will be 11. Middle terms will be( 11 + 1)/ 2 = 6 To find T6, we need to put r = 5 in the formula Tr + 1 = n Cr a n – r b r
T5 + 1 = 10 C5( x / 3) 10-5( 9y) 5
Or T6 = 61236x 5 y 5