
binomial expansion
i just need verification, tell me if i am correct or not. if im incorrect please correct me.
1.By using the binomial expansion, show that:
$\displaystyle (q+p)^n  (qp)^n = 2 (nC1) q^(n1)p + 2 (nC3)q^(n3)p^3 +..... $
i expanded the first two terms of (q+p)^n and (qp)^ n, then i added them together to get the exact statement above. is that fine or do i need a vigorous show to n terms?
2. what is the last term of the expansion if n is odd
if n is odd then the last two terms of (q+p)^n and (qp)^n are added together giving $\displaystyle 2(nCk) p^k $
3. what is the last term of the expansion if n is even
if n is even then the last two terms of $\displaystyle (q+p)^n $ and $\displaystyle (qp)^n $ cancel each other leaving the second last term [tex] 2 (nC(k1)) q. p^(k1)

$\displaystyle (q+p)^n  (qp)^n=$$\displaystyle \sum_{k=0}^{n} \binom{n}{k}\ q^k p^(kn)$$\displaystyle \sum_{k=0}^{n} (1)^n\binom{n}{k}\ q^k p^(kn)$
Now expand the sum..(Happy)