1. total number of terms in the expansion = n+1
2. The sum of indices of x and a in each term is n.
3. the coefficients of terms equidistant from the beginning and the end are equal.
= (r = 0 to n)Σ ((-1) r*nCrxn-rar
The terms in the expansion of(x-a)n are alternatively positive and negative, the last term is positive or negative according as n is even or odd.
5. (1+x) n = (r = 0 to n)Σ nCrxr
you get it by putting x =1 and a = x in the expression for (x+a)n.
6. (x+1) n = (r = 0 to n)Σ nCrxn-r
7. (1-x) n = (r = 0 to n)Σ(-1)r* nCrxr
8. (x+a) n +(x-a) n = 2[nC0xna0 +
9. General term in a binomial expansion
(r+1) term in (x+a) n