Induction proof...I'm stuck!

Hopefully someone can help me with this..I'm nearly done.

I'm in the induction step of the proof & here's what I have:

"So suppose that P(n) holds for *n* an integer and *n*>=5, we have that

2^*n*** >*** n^2.*

We wish to show that P(n+1) holds, that is that

2^(*n*+1) **>** (*n*+1)^2. This can be rewritten as

2(2^*n*) **>** *n*^2 +2*n *+1.

So, by our induction hypothesis and our Lemma (stated & proved earlier before this proof) we have

2(2^n) **> **2^*n ***>** *n*^2 **>** 2*n*+1."

....This is where I'm stuck...is there a property that allows me to then just state "Thus 2(2^*n*) > *n*^2 +2*n* +1"?

Thanx for any feedback you provide!