Posted by **Daisy** on Monday, January 21, 2008 at 10:00pm.

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

- Calculus -
**Reiny**, Monday, January 21, 2008 at 10:38pm
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

- Calculus -
**Reiny**, Monday, January 21, 2008 at 10:43pm
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

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