Compute the coefficient of x^4 in (3x+2)^9.
A.2^5 3^4 C(9,4)
B.2^5 C(9,4)
C.3^4 C(9,4)
D.C(9,4)
Write it as (2 + 3x)^9
Expand:
(2 + 3x)^9 = 2^9 + 9*2^8*(3x) + (9*8/2!)*2^7(3x)^2 + (9*8*7/3!)*2^6*(3x)^3 + (9*8*7*6/4!)*2^5*(3x)^4 + ....
So coefficient of x^4 is (9*8*7*6/4!)*2^5*3^4 → 326592
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I should have noted that A in your list is the right answer.
