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 - (q-p)^n = 2 (nC1) q^(n-1)p + 2 (nC3)q^(n-3)p^3 +..... $

i expanded the first two terms of (q+p)^n and -(q-p)^ 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 -(q-p)^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 -(q-p)^n $ cancel each other leaving the second last term [tex] 2 (nC(k-1)) q. p^(k-1)