Question

Find the constant term in the expansion of [x + (3/x squared)]^9

Find the coefficient of (x)^4(y)^9 in the expansion of (x + (2)(y)^3)^7

Answer 1

for the first one, first of all, find the general term.
I got
C(7,r)x^(7-r)(3/x^2)^r
=c(7,r)(3)^r x^(9-3r)

for that to be a constant the exponent of the x terms must be zero,so
9-3r=0
r=3

so the constant term is C(7,3)(3^3) = 2268

for the second question, to have the x^4, it must be term number 3.
You work this one out, let me know what you got

Answer 2

correction, whenever you see a 7, it should be a 9

so here it is again
for the first one, first of all, find the general term.
I got
C(9,r)x^(9-r)(3/x^2)^r
=c(9,r)(3)^r x^(9-3r)

for that to be a constant the exponent of the x terms must be zero,so
9-3r=0
r=3

so the constant term is C(9,3)(3^3) = 2268