[Urgent] Generating Functions

Hey guys, first time poster here.

I've spent the last couple hours slaving over problems of generating functions and now using them for distributions is giving me trouble.

I've broken the generating series down into the following:

(x^4+x^5+x^6)(x^3+x^4+x^5+x^6+x^7)(1+x+x^2+x^3+..+ ..)

So firstly: (1+x+x^2+..+..) = 1/(1-x)

(x^4+x^5+x^6)(x^3+x^4+x^5+x^6+x^7)(1/(1-x))

Factor out x^4 and x^3 from each polynomial

x^4(1+x+x^2) x^3(1+x+x^2+x^3+x^4) (1/(1-x)

Rewrite both

x^4((1-x^3)/(1-x)) x^3((1-x^5)/(1-x)) (1/1-x)

x^7 ((1-x^3)/(1-x)) ((1-x^5)/(1-x)) (1/(1-x))

And this is where I'm stuck.. where the heck do I go from here?

I'm trying to find out the coefficient of x^10.

This is last minute help, have a quiz on it tomorrow. Thanks guys