Find the coefficient of (i) `x^(5)" in the expansion of "(x+3)^(8)`
(ii) `x^(6) " in the expansion of "(3x^(2) - a/(3x))^(9)`
(iii) `x^(-15) " in the expansion of " (3x^(2) - a/(3x^(3)))^(10).`
(iv) `a^(7)b^(5)" in the expansion of "(a-2b)^(12)`.

Answer

(i) 1512 (ii) 378 (iii) `(-40)/27a^(7)` (iv)-25344

Explanation

(iii) `T_(r+1)= ( - 1)^(r) xx .^(10)C_(r) ( 3x^(2))^((10-r)) xx (a/(3x^(3)))^(r)`
`rArr T_(r+1) = ( -1)^(r) xx . ^(10)C_(r) xx 3 ^((10-r)) xx x^((20 xx 5r)) xx a^(r).`
Now, `20 - 5r = -15 rArr 5r = -15 rArr 5r = 35 rArr r = 7.`
(iv) `T_(r+1) =(-1)^(r) xx .^(12) C _(r) xxa^((12-r)) xx ( 2b)^(r)`
` rArr T_(r+1) = (-1)^(r) xx .^(12)C_(r) xx 2^(r) xx a^((12-r)) b^(r).`
Put`r=5 and " get " T_(6).`