1. For each of the following, simplify so that the variable term is raised is to a single power:(adsbygoogle = window.adsbygoogle || []).push({});

(a) State the General Term tr in the Binomial expansion of (2x^2 - 1/x)^10

(b) Find the 7th term in the expansion

(c) Is there an x^5 term? Find its coefficient.

(d) Is there a constant term [independent of x] ? Find it if there is?

this is what i have so far...

a) tr = C(10,r) (2x^2)^(10-r)*(-1/x)^r

= C(10,r) 2^(10-r) * x^(20-r)* (-1)^r * x^-r

= 2^(10-r) * (-1)^r * C(10,r) * x^(20-3r)

b) Since it is t7, r = 6

so t7 = 2^4 * (-1)^6 * C(10,6) * x^2

= 3360x^2

c) Let 20-3r = 5, so r = 5.

So t5 = 2^5 * (-1)^5 * C(10,5) * x^2

and the coefficient is -8064

d) Let 20-3r = 0

r = 20/3 so there is no constant term?

a somewhat unrelated topic, but another quesiton...

2. http://img161.imageshack.us/img161/4540/explicit9uq.jpg [Broken]

how can i utilize the hints to develop a formula?

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# Binomial theorem

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